Answer
See the graph
Work Step by Step
Given: $y=-2x^2+8x+7$
The coefficients are $a=-2, b=8$, and $c=7$. Because $a\lt0$, the parabola opens down.
Find the vertex.
$x=\frac{-b}{2a}=\frac{-8}{2.(-2)}=2$
Then find the y-coordinate of the vertex.
$y=-2(2)^2+8.2+7=15$
Draw the axis of symmetry $x=2$.
The y-intercept is 7. Plot the point (0,7). Then reflect this point in the axis of symmetry to plot another point, $(4,7)$.
Evaluate the function for another value of x, such as $x=−4$.
$y=-2(1)^2+8(1)+7=13$
Plot the point $(1,13)$ and its reflection $(3,13)$ in the axis of symmetry.
Draw a parabola through the plotted points.
