Question

Write the equation of the quadratic function with roots 6 and 10 and a vertex at (8, 2). Thank you to anyone who helps!

Answer 1

.6 and 10 are roots, so x – 6 and x – 10 are factors.
y = a(x – 6)(x – 10).....plug in the point (8, 2) and solve for a:
2 = a(8 – 6)(8 – 10)
2 = –4a
a = –1/2
...y = (–1/2)(x – 6)(x – 10)
...y = (–1/2)(x² – 16x + 60)
...y = (–x²/2) + 8x – 30 <<<------Answer, or:
...y = (–1/2)(x – 8)² + 2 <<<------Answer