Answer:
x-intercepts are (0, 0) and (-6, 0)
Step-by-step 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)
Answer:
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 )
