Solving Quadratic Inequalities - Math

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Question

Solve the quadratric inequality:

$y\geq $-x^2$+10x-21$

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Answer

Factor and solve.

$y\geq $-x^2$+10x-21$

$y\leq $x^2$-10x+21$

Since the equation is less than or equal to, you know the inequality will be OR, not AND.

$y\leq (x-7)(x-3)$

$x\leq3$ or $x\geq7$

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Question

Solve the following quadratic inequality:

$y\leq $x^2$+4x+3$

Tap to reveal answer

Answer

Factor and solve. Since the sign is less than or equal to, we know the inequality will be OR, not AND.

$y\leq $x^2$+4x+3$

$y\leq (x+3)(x+1)$

$x\leq-3$ or $x\geq -1$

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Question

Solve the following quadratic inequality:

$y\leq $-x^2$+6x+5$

Tap to reveal answer

Answer

Use the quadratic formula to solve.

$y\leq $-x^2$+6x+5$

$y\geq $x^2$-6x-5$

Since the inequality is greater than or equal to, we know the inequality will be AND, not OR.

$x = $\frac{-b \pm $\sqrt{b^2$-4ac}$}{2a}$

$x = $\frac{-(-6) \pm $\sqrt{(-6)^2$-4(1)(-5)}$}{2(1)}$

$x= $\frac{6 \pm \sqrt{56}$}{2}$

$x= 3 \pm $\sqrt{14}$$

$3-$\sqrt{14}$\leq x \leq 3+$\sqrt{14}$$

← Didn't Know|Knew It →

Question

Solve the quadratric inequality:

$y\geq $-x^2$+10x-21$

Tap to reveal answer

Answer

Factor and solve.

$y\geq $-x^2$+10x-21$

$y\leq $x^2$-10x+21$

Since the equation is less than or equal to, you know the inequality will be OR, not AND.

$y\leq (x-7)(x-3)$

$x\leq3$ or $x\geq7$

← Didn't Know|Knew It →

Question

Solve the following quadratic inequality:

$y\leq $x^2$+4x+3$

Tap to reveal answer

Answer

Factor and solve. Since the sign is less than or equal to, we know the inequality will be OR, not AND.

$y\leq $x^2$+4x+3$

$y\leq (x+3)(x+1)$

$x\leq-3$ or $x\geq -1$

← Didn't Know|Knew It →

Question

Solve the following quadratic inequality:

$y\leq $-x^2$+6x+5$

Tap to reveal answer

Answer

Use the quadratic formula to solve.

$y\leq $-x^2$+6x+5$

$y\geq $x^2$-6x-5$

Since the inequality is greater than or equal to, we know the inequality will be AND, not OR.

$x = $\frac{-b \pm $\sqrt{b^2$-4ac}$}{2a}$

$x = $\frac{-(-6) \pm $\sqrt{(-6)^2$-4(1)(-5)}$}{2(1)}$

$x= $\frac{6 \pm \sqrt{56}$}{2}$

$x= 3 \pm $\sqrt{14}$$

$3-$\sqrt{14}$\leq x \leq 3+$\sqrt{14}$$

← Didn't Know|Knew It →

Question

Solve the quadratric inequality:

$y\geq $-x^2$+10x-21$

Tap to reveal answer

Answer

Factor and solve.

$y\geq $-x^2$+10x-21$

$y\leq $x^2$-10x+21$

Since the equation is less than or equal to, you know the inequality will be OR, not AND.

$y\leq (x-7)(x-3)$

$x\leq3$ or $x\geq7$

← Didn't Know|Knew It →

Question

Solve the following quadratic inequality:

$y\leq $x^2$+4x+3$

Tap to reveal answer

Answer

Factor and solve. Since the sign is less than or equal to, we know the inequality will be OR, not AND.

$y\leq $x^2$+4x+3$

$y\leq (x+3)(x+1)$

$x\leq-3$ or $x\geq -1$

← Didn't Know|Knew It →

Question

Solve the following quadratic inequality:

$y\leq $-x^2$+6x+5$

Tap to reveal answer

Answer

Use the quadratic formula to solve.

$y\leq $-x^2$+6x+5$

$y\geq $x^2$-6x-5$

Since the inequality is greater than or equal to, we know the inequality will be AND, not OR.

$x = $\frac{-b \pm $\sqrt{b^2$-4ac}$}{2a}$

$x = $\frac{-(-6) \pm $\sqrt{(-6)^2$-4(1)(-5)}$}{2(1)}$

$x= $\frac{6 \pm \sqrt{56}$}{2}$

$x= 3 \pm $\sqrt{14}$$

$3-$\sqrt{14}$\leq x \leq 3+$\sqrt{14}$$

← Didn't Know|Knew It →

Question

Solve the quadratric inequality:

$y\geq $-x^2$+10x-21$

Tap to reveal answer

Answer

Factor and solve.

$y\geq $-x^2$+10x-21$

$y\leq $x^2$-10x+21$

Since the equation is less than or equal to, you know the inequality will be OR, not AND.

$y\leq (x-7)(x-3)$

$x\leq3$ or $x\geq7$

← Didn't Know|Knew It →

Question

Solve the following quadratic inequality:

$y\leq $x^2$+4x+3$

Tap to reveal answer

Answer

Factor and solve. Since the sign is less than or equal to, we know the inequality will be OR, not AND.

$y\leq $x^2$+4x+3$

$y\leq (x+3)(x+1)$

$x\leq-3$ or $x\geq -1$

← Didn't Know|Knew It →

Question

Solve the following quadratic inequality:

$y\leq $-x^2$+6x+5$

Tap to reveal answer

Answer

Use the quadratic formula to solve.

$y\leq $-x^2$+6x+5$

$y\geq $x^2$-6x-5$

Since the inequality is greater than or equal to, we know the inequality will be AND, not OR.

$x = $\frac{-b \pm $\sqrt{b^2$-4ac}$}{2a}$

$x = $\frac{-(-6) \pm $\sqrt{(-6)^2$-4(1)(-5)}$}{2(1)}$

$x= $\frac{6 \pm \sqrt{56}$}{2}$

$x= 3 \pm $\sqrt{14}$$

$3-$\sqrt{14}$\leq x \leq 3+$\sqrt{14}$$

← Didn't Know|Knew It →

Knew It

Solving Quadratic Inequalities - Math

Solve the quadratric inequality:

Factor and solve. Since the equation is less than or equal to, you know the inequality will be OR, not AND. or

Solve the following quadratic inequality:

Factor and solve. Since the sign is less than or equal to, we know the inequality will be OR, not AND. or

Solve the following quadratic inequality:

Use the quadratic formula to solve. Since the inequality is greater than or equal to, we know the inequality will be AND, not OR.

Solve the quadratric inequality:

Factor and solve. Since the equation is less than or equal to, you know the inequality will be OR, not AND. or

Solve the following quadratic inequality:

Factor and solve. Since the sign is less than or equal to, we know the inequality will be OR, not AND. or

Solve the following quadratic inequality:

Use the quadratic formula to solve. Since the inequality is greater than or equal to, we know the inequality will be AND, not OR.

Solve the quadratric inequality:

Factor and solve. Since the equation is less than or equal to, you know the inequality will be OR, not AND. or

Solve the following quadratic inequality:

Factor and solve. Since the sign is less than or equal to, we know the inequality will be OR, not AND. or

Solve the following quadratic inequality:

Use the quadratic formula to solve. Since the inequality is greater than or equal to, we know the inequality will be AND, not OR.

Solve the quadratric inequality:

Factor and solve. Since the equation is less than or equal to, you know the inequality will be OR, not AND. or

Solve the following quadratic inequality:

Factor and solve. Since the sign is less than or equal to, we know the inequality will be OR, not AND. or

Solve the following quadratic inequality:

Use the quadratic formula to solve. Since the inequality is greater than or equal to, we know the inequality will be AND, not OR.

Solve the quadratric inequality:

$y\geq $-x^2$+10x-21$

Factor and solve.

$y\geq $-x^2$+10x-21$

$y\leq $x^2$-10x+21$

Since the equation is less than or equal to, you know the inequality will be OR, not AND.

$y\leq (x-7)(x-3)$

$x\leq3$ or $x\geq7$

Solve the following quadratic inequality:

$y\leq $x^2$+4x+3$

Factor and solve. Since the sign is less than or equal to, we know the inequality will be OR, not AND.

$y\leq $x^2$+4x+3$

$y\leq (x+3)(x+1)$

$x\leq-3$ or $x\geq -1$

Solve the following quadratic inequality:

$y\leq $-x^2$+6x+5$

Solve the quadratric inequality:

$y\geq $-x^2$+10x-21$

Factor and solve.

$y\geq $-x^2$+10x-21$

$y\leq $x^2$-10x+21$

Since the equation is less than or equal to, you know the inequality will be OR, not AND.

$y\leq (x-7)(x-3)$

$x\leq3$ or $x\geq7$

Solve the following quadratic inequality:

$y\leq $x^2$+4x+3$

Factor and solve. Since the sign is less than or equal to, we know the inequality will be OR, not AND.

$y\leq $x^2$+4x+3$

$y\leq (x+3)(x+1)$

$x\leq-3$ or $x\geq -1$

Solve the following quadratic inequality:

$y\leq $-x^2$+6x+5$

Solve the quadratric inequality:

$y\geq $-x^2$+10x-21$

Factor and solve.

$y\geq $-x^2$+10x-21$

$y\leq $x^2$-10x+21$

Since the equation is less than or equal to, you know the inequality will be OR, not AND.

$y\leq (x-7)(x-3)$

$x\leq3$ or $x\geq7$

Solve the following quadratic inequality:

$y\leq $x^2$+4x+3$

Factor and solve. Since the sign is less than or equal to, we know the inequality will be OR, not AND.

$y\leq $x^2$+4x+3$

$y\leq (x+3)(x+1)$

$x\leq-3$ or $x\geq -1$

Solve the following quadratic inequality:

$y\leq $-x^2$+6x+5$

Solve the quadratric inequality:

$y\geq $-x^2$+10x-21$

Factor and solve.

$y\geq $-x^2$+10x-21$

$y\leq $x^2$-10x+21$

Since the equation is less than or equal to, you know the inequality will be OR, not AND.

$y\leq (x-7)(x-3)$

$x\leq3$ or $x\geq7$

Solve the following quadratic inequality:

$y\leq $x^2$+4x+3$

Factor and solve. Since the sign is less than or equal to, we know the inequality will be OR, not AND.

$y\leq $x^2$+4x+3$

$y\leq (x+3)(x+1)$

$x\leq-3$ or $x\geq -1$

Solve the following quadratic inequality:

$y\leq $-x^2$+6x+5$