All SSAT Upper Level Math Resources
Example Questions
Example Question #511 : Ssat Upper Level Quantitative (Math)
A horizontal parabola on the coordinate plane has vertex ; one of its
-intercepts is
.
Give its equation.
Insufficient information is given to determine the equation.
The equation of a horizontal parabola, in vertex form, is
,
where is the vertex. Set
:
To find , use the known
-intercept, setting
:
The equation, in vertex form, is ; in standard form:
Example Question #512 : Ssat Upper Level Quantitative (Math)
A vertical parabola on the coordinate plane has -intercepts
and
, and passes through
.
Give its equation.
Insufficient information is given to determine the equation.
A horizontal parabola which passes through and
has as its equation
.
To find , substitute the coordinates of the third point, setting
:
The equation is therefore , which is, in standard form:
Example Question #515 : Ssat Upper Level Quantitative (Math)
A vertical parabola on the coordinate plane has -intercepts
and
, and passes through
.
Give its equation.
A vertical parabola which passes through and
has as its equation
To find , substitute the coordinates of the third point, setting
:
The equation is ; expand to put it in standard form:
Example Question #12 : How To Find The Equation Of A Curve
A horizontal parabola on the coordinate plane has -intercept
; one of its
-intercepts is
.
Give its equation.
Insufficient information is given to determine the equation.
Insufficient information is given to determine the equation.
The equation of a horizontal parabola, in standard form, is
for some real .
is the
-coordinate of the
-intercept, so
, and the equation is
Set :
However, no other information is given, so the values of and
cannot be determined for certain. The correct response is that insufficient information is given.
Example Question #241 : Coordinate Geometry
A vertical parabola on the coordinate plane includes points and
.
Give its equation.
The standard form of the equation of a vertical parabola is
If the values of and
from each ordered pair are substituted in succession, three equations in three variables are formed:
The system
can be solved through the elimination method.
First, multiply the second equation by and add to the third:
Next, multiply the second equation by and add to the first:
Which can be divided by 3 on both sides to yield
Now solve the two-by-two system
by substitution:
Back-solve:
Back-solve again:
The equation of the parabola is therefore
.
Example Question #14 : How To Find The Equation Of A Curve
A vertical parabola on the coordinate plane shares one -intercept with the line of the equation
, and the other with the line of the equation
. It also passes through
. Give the equation of the parabola.
The correct answer is not among the other responses.
First, find the -intercepts—the points of intersection with the
-axis—of the lines by substituting 0 for
in both equations.
is the
-intercept of this line.
is the
-intercept of this line.
The parabola has -intercepts at
and
, so its equation can be expressed as
for some real . To find it, substitute using the coordinates of the third point, setting
:
.
The equation is , which, in standard form, can be rewritten as:
Example Question #15 : How To Find The Equation Of A Curve
A horizontal parabola on the coordinate plane includes points
, and
.
Give its equation.
The standard form of the equation of a horizontal parabola is
If the values of and
from each ordered pair are substituted in succession, three equations in three variables are formed:
The three-by-three linear system
can be solved by way of the elimination method.
can be found first, by multiplying the first equation by
and add it to the second:
Substitute 5 for in the last two equations to form a two-by-two linear system:
The system
can be solved by way of the substitution method;
Substitute 2 for in the top equation:
The equation is .
Example Question #1 : How To Find The Equation Of A Circle
Give the equation of the above circle.
None of the other choices is correct.
A circle with center and radius
has equation
The circle has center and radius 5, so substitute:
Example Question #2 : How To Find The Equation Of A Circle
A circle on the coordinate plane has a diameter whose endpoints are and
. Give its equation.
A circle with center and radius
has equation
The midpoint of a diameter of the circle is its center, so use the midpoint formula to find this:
Therefore, and
The radus is the distance between the center and one endpoint, so take advantage of the distance formula using and
. We will concern ourcelves with finding the square of the radius
:
Substitute:
Example Question #1 : Circles
Give the equation of the above circle.
A circle with center and radius
has equation
The circle has center and radius 4, so substitute:
All SSAT Upper Level Math Resources
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