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4-121.

For each equation below, find the $x$- and $y$-intercepts and the locator point $\left(h, k\right)$, then write the equations in graphing form.

1. $y = 7 + 2x^{2} + 4x − 5$

y-intercept: $y = 7 + 2\left(0\right)^{2} + 4\left(0\right) − 5$

You will need to factor. There is only one x-intercept.

x-intercept:$0 = 7 + 2x^{2} + 4x − 5$

Since there is only one x-intercept, the vertex must be at the x-intercept. To find the equation in graphing form, use the equation $y = a\left(x − h\right)^{2} +k$.

y-intercept: $\left(0, 2\right)$
x-intercept: $\left(−1, 0\right)$
vertex:$\left(−1, 0\right)$
$y = 2\left(x + 1\right)^{2}$

1. $x^{2} = 2x + x\left(2x − 4\right) + y$

Start by finding the x- and y-intercepts.

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.

Now write the equation in graphing form.