Which of the following are the x-intercepts on the graph of the function shown below? Check all that apply.

Question

1. Which of the following are the x-intercepts on the graph of the function shown below? Check all that apply.
F(x)=2(x+1)(x-2)
-1
2
-4
-2

2. Which function will produce the same graph as the function shown below? Y=(x+1)(x-3)
Y=x^2+2x+3
Y=x^2-2x-3
y-3=(x-1)^2
y+3=x(x-1)

3. What is the equation of the axis of symmetry for the function shown below?
y-1=-2(x+3)^2
x = 3
x = -3
x = -2
y = 7

4. Which point lies on the graph of the function shown below?
Y=-x^2+4x-2
(-1,3)
(0,2)
(1,1)
(2,-2)

Answer 1

1.  X-intercepts on the graph correspond to zeros of the function, so you need to solve F(x)=2(x+1)(x-2)=0. So the two answers are -1 and +2.

 

2. Using the FOIL method to multiply polynomials, Y=(x+1)(x-3)=x^2-2x-3.

 

3. The function is a downward-opening parabola with a vertex at (-3,1). The line of symmetry passes vertically through the vertex, and is therefore x=-3.

 

4. Plug each x into the function, and the only one that comes up with the proper y is (1,1): 1=-(1^2)+4(1)-2.