## Related questions with answers

Question

Find the vertex, the $y$-intercept, and symmetric point, and use these to sketch the graph.

$y=8 x^2+40 x+37$

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 7To find the vertex, transform the equation to $y=a(x-h)^2+k$ in which vertex has the coordinates $V(h,k)$. First complete the square.

$\begin{aligned} y&= (8x^2+40x)+37\\\\&=8\bigg(x^2+5x+\dfrac{25}{4}\bigg)-8\cdot\dfrac{25}{4}+37\\ \\&=8\bigg(x+\dfrac{5}{2}\bigg)^2-13\\\\&=8\bigg(x+\dfrac{5}{2}\bigg)^2-13 \end{aligned}$

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