Question

Determine the coordinates of the vertex and horizontal intercepts of the parabola. (If an answer does not exist, enter DNE.)

f(x) = −7(x + 12)2 + 14
I cant figure out the horizontal intercepts.

Answer 1

f(x) = −7(x + 12)² + 14
the coordinates of the vertex are (-12;14)
f(x)=-7(x²+24x-144)+14
f(x)=-7x²-168x+1008+14
f(x)=-7x²-168x+1022=0
7x²+168x-1022=0
x=
`\frac{-168+- \sqrt{ 168^(2) +4*7*1022} }{14}`=
`(-168+- √(56840) )/(14)`=
`(-168+-14 √(290) )/(14)`=-12+-√290
x₁=-12-√290
x₂=-12+√290
Answer: the coordinates of the vertex are (-12;14),
horizontal intercepts are x₁=-12-√290, x₂=-12+√290