CPM Homework Help : INT3 Problem 7-61

For each function, determine the $x$ - and $y$ -intercepts and the locator point ( $h, k$ ). If you have not already done so, write the equations in graphing form.

$y = 7 + 2x^{2} + 4x - 5$
Step 1(a):
$y$ -intercept: $y = 7 + 2\left(0\right)^{2} + 4\left(0\right) − 5$
Step 2(a):
$x$ -intercept: $0 = 7 + 2x^{2} + 4x − 5$
More Help (a):
Since there is only one $x$ -intercept, the vertex must be at the $x$ -intercept.
Answer (a):
$y$ -intercept: $\left(0, 2\right)$
$x$ -intercept: $\left(−1, 0\right)$
vertex: $\left(−1, 0\right)$
$y = 2\left(x + 1\right)^{2}$

$x^{2} = 2x + x\left(2x - 4\right) + y$
Hint (b):
Start by determining the $x$ - and $y$ -intercepts.
More Help 1(b):
To find the $x$ -coordinate of the vertex, average the $x$ -intercepts.
To find the $y$ -coordinate of the vertex, substitute the $x$ -coordinate of the vertex into the given equation and solve for $y$ .
More Help 2(b):
Now write the equation in graphing form.