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)
