What are the vertex and x-intercepts of the graph of the function given below? y = x2 - 2x - 35
A. Vertex: (1, -25); x-intercepts: (
6,0) and (-4,0)
B. Vertex: (7,5); x-intercepts: (7,0) and (8,0)
C. Vertex: (0,0); x-intercepts: (-4,0) and (-5,0)
D. Vertex: (1, -36); x-intercepts: (7,0) and (-5,0)

D

Step-by-step explanation:

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

= -

y = x² - 2x - 35 ← is in standard form

with a = 1 and b = - 2 , thus

= - = 1

Substitute x = 1 into y for corresponding coordinate of y

y = 1² - 2(1) - 35 = 1 - 2 - 35 = - 36

vertex = (1, - 36 )

To find the x- intercepts let y = 0, that is

x² - 2x - 35 = 0

Consider the factors of the constant term (- 35) which sum to give the coefficient of the x- term (- 2)

The factors are - 7 and + 5, since

- 7 × 5 = - 35 and - 7 + 5 = - 2, thus

(x - 7)(x + 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 5 = 0 ⇒ x = - 5

x- intercepts are (7, 0 ) and (- 5, 0 )

x=30

step-by-step explanation: