Question

Question #53a4c

Answer 1

The vertex of the parabola `y = -4x^2 + 8x - 7` is (1, -3).

Right away it's important to realize that this is a quadratic equation of the form `y = ax^2 + bx + c`, so it will form a parabola.

The line of symmetry (or axis that passes through the vertex) of the parabola will always be -b/2a. "B" in this case is 8, and "a" is -4, so `-b/(2a)` = `-8/(2(-4))`=`(-8)/-8`=`1`

This means the x value of the vertex will be 1. Now, all you have to do to find the y-coordinate is plug '1' in for x and solve for y:

`y=-4(1)^2 + 8(1) - 7`
`y = -4 + 8 - 7`
`y = -3`

So the vertex is (1, -3), as seen in the graph below (roll over the vertex to see the coordinates). graph{-4x^2 + 8x - 7 [-8.46, 11.54, -9.27, 1.15]}