Question

Find the x-intercept(s) and the coordinates of the vertex for the parabola y= x^2 -8x + 12. if there is more than one x-intercept, separate them with commas.

Answer 1

Answer:

(i) x-intercepts: (2, 0), (6, 0)

(ii) vertex : (4, -4)

Explanation:

y = x² - 8x + 12

To find x intercepts, [set y = 0]

• x² - 8x + 12 = 0

• x² - 2x - 6x + 12 = 0

• x(x - 2) - 6(x - 2) = 0

• (x - 6)(x - 2) = 0

• x = 6, x = 2

x-intercepts: (2, 0), (6, 0)

To find vertex:

x = -b/2a

  = -(-8)/2(1)

  = 4

y = x² - 8x + 12

  = 4² - 8(4) + 12

  = -4

Vertex : (4, -4)

Answer 2

Solve the equation for y=0

• x²-8x+12=0
• x²-6x-2x+12=0
• x(x-6)-2(x-6)=0
• (x-2)(x-6)=0
• x=2,6

X inetercepts (2,0) and (6,0)

Vertex :-

x coordinate

• -b/2a
• 8/2
• 4

Y coordinate

• 4²-8(4)+12
• -4

Verted at (4,-4)