Question

Find the x-intercepts of the parabola with

vertex (-3,-18) and y-intercept (0,0).
Write your answer in this form: (X1,Y1),(X2,42).
If necessary, round to the nearest hundredth.

Answer 1

The x-intercepts are ( 0 , 0 ) , ( -6 , 0 )

Explanation:

vertex (-3,-18) and y-intercept (0,0)

equation used f(x) = a(x - h)² + k where (h,k) is vertex.

0 = a(0--3)² + -18

0 = 9a - 18

18 = 9a

a = 2

f(x) = a(x - h)² + k ......this is vertex to find equation of parabola.

f(x) = 2(x - -3)² + -18

f(x) = 2(x + 3)² - 18 ....this is our formula of parabola

f(x) = 2(x² +6x + 9) - 18

f(x) = 2x² +12x +18 - 18

f(x) = 2x²+12x .....if simplified.

To find x intercepts, y must be 0,

2x²+12x = 0

2x(x+6) = 0

x = 0 , -6

so the coordinates are: ( 0 , 0 ) , ( -6 , 0 )

Answer 2

x-intercepts are (0, 0) and (-6, 0)

Explanation:

equation of a parabola in vertex form: y = a(x - h)² + k

where (h, k) is the vertex

Substituting the given vertex (-3, -18) into the equation:

y = a(x + 3)² - 18

If the y-intercept is (0, 0) then substitute x=0 and y=0 into the equation and solve for a:

0 = a(0 + 3)² - 18

⇒ 0 = a(3)² - 18

⇒ 0 = 9a - 18

⇒ 9a = 18

⇒ a = 2

Therefore, y = 2(x + 3)² - 18

To find the x-intercepts, set the equation to 0 and solve for x:

2(x + 3)² - 18 = 0

Add 18 to both sides: 2(x + 3)² = 18

Divide both sides by 2: (x + 3)² = 9

Square root both sides: x + 3 = ±3

Subtract 3 from both sides: x = ±3 - 3

so x = 3 - 3 = 0

and x = -3 - 3 = -6

So x-intercepts are (0, 0) and (-6, 0)