Graph the following quadratic equation by first completing the square: y= −2𝑥+ 6𝑥 + 7.

Answer 1

-2x^2 + 6x + 7
= -2(x^2-3x) + 7
= -2(x^2 - 3x + 9/4) + 7 + 2(9/4)
= -2(x - 3/2)^2 + 23/2
so the vertex is at (3/2, 23/2) and it opens downward
per the Quadratic Formula, the roots are at
x = (3±√23)/2