Question

What are the vertex and x intercepts of the graph of y=(x+4)(x-2)? Select one answer for the vertex and one for the x intercepts.
A.x intercepts (-4,0) ,(2,0)
B.x intercepts (-4,0)(-2,0)
C.vertex (1,9)
D.vertex (-1,-5)
E.vertex (-1,-9)
F.x intercepts (4,0),(-2,0)

Answer 1

Answer:

The x-intercepts points are (-4 , 0) , (2 , 0) ⇒ answer (A)

The vertex point is (-1 , -9) ⇒ answer (E)

Step-by-step explanation:

* Lets revise the quadratic equation

 y = ax² + bx + c

- To find the x-intercepts put y = 0

- To find the vertex use the rule:

# x-coordinate of the vertex of the parabola which represents

  the quadratic function graphically = -b/2a

# To find the y-coordinate substitute the value of the x-coordinate

  of the vertex in the equation

* Lets use these information to solve the problem

∵ y = (x + 4)(x -2)

- To find the x-intercepts let y = 0

∴ (x + 4)( x - 2) = 0 ⇒ put each bracket = 0

∴ x + 4 = 0 and x - 2 = 0

∵ x + 4 = 0 ⇒ subtract 4 from the both sides

∴ x = -4

∵ x - 2 = 0 ⇒ add 2 to both sides

∴ x = 2

* The x-intercepts points are (-4 , 0) , (2 , 0)

- Now lets use the foil method to multiply the two brackets

∵ (x + 4)(x - 2) = x² - 2x + 4x - 8 ⇒ collect the like terms

∴ (x + 4)(x - 2) = x² + 2x - 8

∴ y = x² + 2x - 8

* Now lets find the value of a and b to find the x-coordinate

 of the vertex point

∵ a = 1 , b = 2

∵ x-coordinate of the vertex = -b/2a

∴ x = -2/2(1) = -1

- Substitute the value of x in y

∴ y = (-1)² + 2(-1) - 8 = 1 - 2 - 8 = -9

∴ The vertex point is (-1 , -9)

* The vertex point is (-1 , -9)