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Home > A2C > Chapter 7 > Lesson 7.3.2 > Problem 7-175

7-175.

Change each equation to graphing form. Sketch the graph and label each vertex and axis of symmetry.

$y = 2x^2 + 7x - 7$
Step 1(a):
Add $7$ to both sides to isolate the $x$ -terms.
$y+7=2x^2+7x$
Step 2(a):
Factor out a $2$ from the $x$ -terms.
$y+7=2\left(x^2+\frac{7}{2}x \right)$
Step 3(a):
Complete the square. Remember to add to both sides.
$y+7+\frac{98}{16}=2\left( x^2+\frac{7}{2}x+\frac{49}{16} \right)$
Step 4(a):
Simplify.
$y+\frac{105}{8}=2\left( x+\frac{7}{4} \right)^2$
Hint (a):
Where is the vertex? Axis of symmetry?

$y = 3x^2 - x - 8$
Hint (b):
See part (a).

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