Accuplacer College Level Math Study Guide

Running head: MAT-121/ College Algebra
MAT-121/ College Algebra
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MAT-121/ College Algebra 1
SECTION 5.1:
1.
Step 1: Group the first 2 terms together, separating them from the constant term.
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Step 2: Factor out leading coefficient, for completing the square to work, the coefficient
of x2 must be 1.
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Step 3: Complete the square, Take half of x coefficient and square it. Notice to keep
equation balanced you must add this number and subtract it making the net effect zero.
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Step 4: Distribute and add constants.
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Now it is successfully in vertex form and can be easily graphed.
The vertex is at (-0.625,-8.5625)

MAT-121/ College Algebra 2
The parabola opens up and has a y-intercept at (0, -7)
Here is a graph of this parabola:
2.
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Step 1: Group the first 2 terms together, separating them from the constant term.
-->
Step 2: Factor out leading coefficient, for completing the square to work, the coefficient
of x2 must be 1.
-->
Step 3: Complete the square, Take half of x coefficient and square it. Notice to keep

MAT-121/ College Algebra 3
equation balanced you must add this number and subtract it making the net effect zero.
-->
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Step 4: Distribute and add constants.
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Now it is successfully in vertex form and can be easily graphed.
The vertex is at (2, 5)
The parabola opens up and has a y-intercept at (0, 9)
The axis of symmetry splits the parabola in 2 equal parts. It runs through the vertex straight
up and down (for a parabola that either opens up or opens down). And so we can write an
equation for the line that is vertical and runs through the vertex. In this question, it's x=2.
3.
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Step 1: Group the first 2 terms together, separating them from the constant term.

MAT-121/ College Algebra 4
-->
Step 2: Factor out leading coefficient, for completing the square to work, the coefficient of
x2 must be 1.
-->
Step 3: Complete the square, Take half of x coefficient and square it. Notice to keep equation
balanced you must add this number and subtract it making the net effect zero.
-->
-->
Step 4: Distribute and add constants.
-->
-->
Now it is successfully in vertex form and can be easily graphed.

MAT-121/ College Algebra 5
The vertex is at (2,2)
The parabola opens down and has a y-intercept at (0, -2)
Since we know the maximum value is y=2, all y values less than and including 2 will be part
of the parabola graph.
y≤2
4.
Vertex form of a quadratic
y = a(x - h)2 + k
here,
(h, k) = (−1 , 3),
( x, y) = (−2 , 6)
y = a(-2+1)2 + 3
 6 = a + 3