Question

What are the vertex and x-intercepts of the graph of the function given below?

y = x^2 – 2x – 35

A. Vertex: (1, –36); x-intercepts: (7, 0) and (–5, 0)
B. Vertex: (7, 5); x-intercepts: (7, 0) and (8, 0)
C. Vertex: (1, –25); x-intercepts: (6, 0) and (–4, 0)
D. Vertex: (0, 0); x-intercepts: (–4, 0) and (–5, 0)

Answer 1

the correct question is
What are the vertex and x-intercepts of the graph of the function given below?
y = x²-2x-35

step 1
convert the equation in the vertex form
y+35=x²-2x
y+35=(x²-2x+1-1)
y+35+1=(x²-2x+1)
y+36=(x-1)²------> equation in the vertex form

the vertex is the point (1,-36)

the answer Part a) is
the vertex is the point (1,-36)

Part b) Find the x-intercepts
we know that
the x-intercepts is when y=0
so
y+36=(x-1)²
for y=0
(x-1)²=36
(+/-)(x-1)=√36-------> (+/-)(x-1)=6
(+)(x-1)=6------> x=6+1-----> x=7
(-)(x-1)=6-----> x=1-6-----> x=-5

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

the answer part b) is
the x-intercepts are the points (7,0) and (-5,0)

the total answer is the option
A. Vertex: (1, -36); x-intercepts: (7, 0) and (-5, 0)