Write an equation of a parabola in vertex form that passes through (7, -17) and has a vertex (4, 1)

Step-by-step explanation:

f(x) = a(x - h)² + k  - the vertex form of an equation of a parabola with vertex (h, k)

(4, 1)  ⇒  h = 4.   k = 1

f(x) = a(x - 4)² + 1   - the vertex form of an equation of the parabola with vertex (4, 1)

the parabola passes through (7, -17)  ⇒ x=7,  f(x)=-17

-17 = a(7 - 4)² + 1

-17 -1 = a(3)² + 1 -1

-18 = 9a

a = -2

The equation of the parabola in vertex form that passes through (7, -17) and has a vertex (4, 1):

                              f(x) = -2(x - 4)² + 1

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11

thus, the first answer choice, y = sec x, is the correct one