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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1511 : Intermediate Geometry

What is the -intercept of the following line:

y=4x-8

Possible Answers:

Correct answer:

Explanation:

The -intercept is the point where the y-value is equal to 0. Therefore,

0=4x-8

4x=8

x=2

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Example Question #1512 : Intermediate Geometry

Which of the following statements regarding the x and y intercepts of the equation y=x^2-6x+9 is true?

Possible Answers:

The x-intercept is greater than the y-intercept.

The graph does not cross the x-axis.

The y-intercept is greater than the x-intercept.

The graph does not cross the y-axis.

The x and y intercepts are equal.

Correct answer:

The y-intercept is greater than the x-intercept.

Explanation:

To find the x-intercept, we simply plug y=0 into our function. giving us 0=x^2-6x+9 . We can factor that equation, making it 0=(x-3)^2 . We can not solve for , and we get x=3 . To find the y-intercept, we do the same thing, however this time, we plug in x=0 instead. This leaves us with y=9 . With an x-intercept of and a y-intercept of , it is clear that the y-intercept is greater than the x-intercept.

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Example Question #1 : How To Find X Or Y Intercept

Find the -intercept of the following function.

y=3x-9

Possible Answers:

x=3

DNE

x=0

x=-9

Correct answer:

x=3

Explanation:

To find the x-intercept, set y equal to 0.

0 = 3x-9

Now solve for x by dividing by 3 on both sides.

9 = 3x

$\frac{9}{3}=\frac{3}{3}x$

This reduces to,

3=x

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Example Question #1513 : Intermediate Geometry

Find the -intercept of the following function.

y=x^2+x-9

Possible Answers:

y=-9

y=9

y=2

y=0

Correct answer:

y=-9

Explanation:

To find the y-intercept, set x equal to 0.

y = 0^2 +0 - 9

Now solve for y.

y=-9

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Example Question #3 : How To Find X Or Y Intercept

Which is the x-intercept for the line $\small y = 2x - 5$ ?

Possible Answers:

$\small -5$

$\small 2.5$

$\small -2.5$

$\small 5$

Correct answer:

$\small 2.5$

Explanation:

The x-intercept of a line is the x-value where the line hits the x-axis. This occurs when y is 0. To determine the x-value, plug in 0 for y in the original equation, then solve for x:

$\small 0 = 2x - 5$ add 5 to both sides

$\small 5 = 2x$ divide by 2

$\small 2.5 = x$

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Example Question #4 : How To Find X Or Y Intercept

Find the x-intercept(s) for the circle $\small (x-4)^2 + y^2 = 9$

Possible Answers:

$\small 1, 7$

$\small 7$

$\small -5, 5$

$\small -1, 7$

The circle never intersects the x-axis

Correct answer:

$\small 1, 7$

Explanation:

The x-intercepts of any curve are the x-values where the curve is intersecting the x-axis. This happens when y = 0. To figure out these x-values, plug in 0 for y in the original equation and solve for x:

$\small (x-4)^2 + 0^2 = 9$ adding 0 or 0 square doesn't change the value

$\small (x-4)^2 = 9$ take the square root of both sides

$\small x - 4 = \pm 3$ this means there are two different potential values for x, and we will have to solve for both. First:

x - 4 = -3 add 4 to both sides

$\small x = 1$

Second: $\small x - 4 = 3$ again, add 4 to both sides

x = 7

Our two answers are x = 1 and x = 7 .

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Example Question #1 : X And Y Intercept

Give the coordinate pair(s) where $\small \small (y+3)^2 - (x-2)^2 = 21$ intersects with the y-axis.

Possible Answers:

$\small (0, 8)$

$\small (0, \pm \sqrt{17}-3)$

$\small (2, 0 )$

$\small (0, 2)$ and $\small (0, -8)$

The graph does not intersect with the y-axis.

Correct answer:

$\small (0, 2)$ and $\small (0, -8)$

Explanation:

To find where the graph hits the y-axis, plug in 0 for x:

$\small (y+3)^2 - (0-2)^2 = 21$ first evaluate 0 - 2

$\small (y+3)^2 - (-2)^2 = 21$ then square -2

$\small (y+3)^2 - 4 = 21$ add 4 to both sides

$\small (y+3)^2 = 25$ take the square root of both sides

$\small y + 3 = \pm 5$ now we have 2 potential solutions and need to solve for both

a) $\small y + 3 = 5$

$\small y = 2$

b) $\small y +3 = -5$

$\small y = -8$

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Example Question #2 : X And Y Intercept

Which is neither an x- or y-intercept for the parabola $\small y = x^2 - 16$

Possible Answers:

$\small -4$

$\small -16$

$\small 4$

Correct answer:

Explanation:

The y-intercept(s) occur where the graph intersects with the y-axis. This is where x=0, so we can find these y-values by plugging in 0 for x in the equation:

$\small y = 0^2 - 16$

$\small y = -16$

The x-intercept(s) occur where the graph intersects with the x-axis. This is where y=0, so we can find these x-values by plugging in 0 for y in the equation:

$\small 0 = x^2 - 16$ add 16 to both sides

$\small 16 = x^2$ take the square root

$\small \pm 4 = x$

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Example Question #11 : X And Y Intercept

What is the x-intercept of the line $y = -\frac{2}{3}x + 6$

Possible Answers:

(-6,0)

(4,0)

(9,0)

(6,0)

(-1.5, 0 )

Correct answer:

(9,0)

Explanation:

To determine the x-intercept, plug in for , since the x-axis is where y=0 .

$0 = -\frac{2}{3} x + 6$ subtract from both sides

$-6 = -\frac{2}{3} x$ multiply both sides by

- 18 = -2 x divide both sides by

9 = x

The x-intercept is (9,0)

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Example Question #11 : How To Find X Or Y Intercept

What is the x-intercept for the line y = -2x-4 ?

Possible Answers:

(-2,0)

(-8,0)

(-4,0)

(4,0)

(2,0)

Correct answer:

(-2,0)

Explanation:

To find the x-intercept, plug in for , since the x-axis is where y = 0 .

0 = -2x- 4 add to both sides

4 = -2x divide both sides by

-2 = x

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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1511 : Intermediate Geometry

Example Question #1512 : Intermediate Geometry

Example Question #1 : How To Find X Or Y Intercept

Example Question #1513 : Intermediate Geometry

Example Question #3 : How To Find X Or Y Intercept

Example Question #4 : How To Find X Or Y Intercept

Example Question #1 : X And Y Intercept

Example Question #2 : X And Y Intercept

Example Question #11 : X And Y Intercept

Example Question #11 : How To Find X Or Y Intercept

All Intermediate Geometry Resources

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