Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). The vertex of a parabola is (-2, -20), and its y-intercept is (0, -12). The equation of the parabola is y =__x^2 +
__ x +__.

Answer 1

Answer: $y = 2 x^2 + 8x - 12$

Step-by-step explanation:

Since the equation of parabola along x-axis is,

$y = a(x-h)^2 + k$

Where (h,k) is the vertex of the parabola and a is any point.

Here, The vertex of a parabola is (-2, -20),

Therefore the equation of parabola is,

$y = a(x+2)^2 -20$

Since, y-intercept is (0, -12),

Therefore, (0,-12) will satisfy the equation of the parabola,

By putting x=0 and y=-12 in the equation of parabola,

$-12 = a(0+2)^2 -20$

⇒ $-12 + 20 = a(0+2)^2$ ( by adding 12 on both sides )

⇒ 8 = 4 a

⇒ a = 2 ( dividing by 4 on both sides )

Thus, the complete equation of parabola is,

$y = 2(x+2)^2 - 20$

⇒ $y = 2 (x^2+4x + 4) - 20$

⇒ $y = 2x^2 + 8x +8 - 20$

⇒  $y = 2x^2 + 8x - 12$

Answer 2

Vertex form:
y-k=a(x-h)^2
h=-2,k=-20,y=-12 when x=0
thus;
-12+20=a(0+2)^2
8=4a
a=2
Equation:
y+20=2(x+2)^2
y+20=2(x^2+4x+4)
f(x)=2(x^2+4x+4)-20
f(x)=2x^2+8x+8-20
f(x)=2x^2+8x-20