Question

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Answer 1

x intercepts: (1,0), (-3,0)

the roots are 1 and -3

Explanation:

Using the Quadratic Formula:

x=−b±sqrt(b2−4ac)/2a

Substitute:

x= -8±sqrt(8^2-4(4)(-12))/2(4)

x=-8±sqrt((64- -192))/8

x=-8±sqrt(256)/8

Solve two equations (±)

x=-8±16/8

x=8/8 and x=-24/8

x=1 and x=-3

Answer 2

x = -3

x = 1

Explanation:

Hello!

We can solve the quadratic by Factoring the Equation and using the Zero Product Property.

Factor

• 
  `y = 4x^2 + 8x - 12`
• 
  `y = 4(x^2 + 2x - 3)`

We want to find two numbers that multiply out to -3, but add up to 2. The numbers that work are -1 and 3. We can expand 2x to -x and 3x and factor by grouping.

• 
  `y = 4(x^2 -x + 3x - 3)`
• 
  `y = 4(x(x - 1) + 3(x - 1))`
• 
  `y = 4(x + 3)(x - 1)`

Solve for x

Set each factor to 0 and solve for x in both.

• 
  `0 = 4(x + 3)(x - 1)`
• 
  `0 = (x + 3), x = -3`
• 
  `0 = (x - 1), x = 1`

Therefore, the x-interecpts are -3 and 1.