Question

Can someone please answer this, ill give you brainliest Would be very appreciated.

Answer 1

Answer:

1. (4, 0) and (-2, 0)
2. (1, -9)
3. (0, -8)

Step-by-step explanation:

Finding the x-intercepts :

• y-value of the x-intercept is 0
• 0 = (x - 4)(x + 2)
• x - 4 = 0 ⇒ x = 4
• x + 2 = 0 ⇒ x = -2
• The x-intercepts are : (4, 0) and (-2, 0)

Finding the vertex :

• Expanding the function f
• f(x) = (x - 4)(x + 2)
• f(x) = x² - 4x + 2x - 8
• f(x) = x² - 2x - 8
• Vertex = (h, k)
• h = -b/2a = -(-2)/2(1) = 1
• k = (1)² - 2(1) - 8
• k = 1 - 2 - 8 = -9
• The vertex is : (1, -9)

Finding the y-intercept :

• Substitute x = 0 in the function
• f(0) = 0² - 2(0) - 8
• f(0) = -8
• The y-intercept is : (0, -8)

Answer 2

Function: f(x) = (x- 4)(x + 2)

1) What are the x-intercepts of the graph?

In order to find x-intercept, the f(x) or y will be 0

=================

(x-4)(x + 2) = 0

(x-4) = 0, (x + 2) = 0

x = 4, x = -2

x intercepts: (4, 0) and (-2, 0)

2) What is the ordered pair of the vertex?

In order to find vertex use the formula: x = -b/2a

y = (x-4)(x + 2)

y = x² -4x + 2x -8

y = x² - 2x -8

Now find x-coordinate of vertex:

x = -(-2)/2(1)

x = 2/2

x = 1

y coordinates: (1-4)(1 + 2) =  -9

Ordered pair of vertex: (1, -9)

3) What is the y intercepts of the graph?

In order to find y intercept, insert x = 0

y = (0-4)(0 + 2)

y = -8

y intercept: (0, -8)