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What are the vertex and x-intercepts of the graph of the function given below?
y = x2 - 2x - 24

A. Vertex: (7, 5); intercepts: x = 6, 8
B. Vertex: (-1, -21); intercepts: x = 6, 4
C. Vertex: (0, 0); intercepts: x = -4, 6
D. Vertex: (1, -25); intercepts: x = 6, -4

Respuesta :

ghanami
hello : 
x²-2x-24 =( x²-2x+1)-1-24 
              = (x-1)² -25 .....    ( vertex form)
. Vertex: (1, -25);
 intercepts: x = 6, -4 because :
f(x) = 0.....        (x-1)² -25 =0
(x-1)² = 5²
x-1=5 or x-1 = -5
x=6 or x=-4

The Vertex is (1, -25) , Intercept is 6 , -4 , Option D is the correct answer.

What is a parabola ?

Parabola is a U shaped curve that has all its points at a fixed distance from a point called as focus and a line called as directrix

It is given that

x²-2x-24

The standard equation of a parabola is

y = a(x-h)² +k

The given equation can be written in this form.

y=( x²-2x+1) -1-24

y= (x-1)² -25

Therefore Vertex is (1, -25)

f(x) = 0

(x-1)² -25 =0

(x-1)² = 5²

x-1=5 or x-1 = -5

x=6 or x= -4

Intercept is 6 , -4

Therefore Option D is the correct answer.

To know more about Parabola

https://brainly.com/question/4074088

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