Question

Need help ASAP 30PT. 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

The equation of the parabola is y = 2(x + 2)² - 20.

Step-by-step explanation:

The given information tells us that the parabola has a vertex at (-2, -20) and a y-intercept at (0, -12). Since the vertex form of a parabola is given by y = a(x - h)² + k, where (h, k) represents the vertex, we can substitute the given values to find the equation of the parabola:

y = a(x - (-2))² + (-20) -> y = a(x + 2)² - 20

Next, we use the y-intercept to determine the value of 'a'. Substituting (0, -12) into the equation:

-12 = a(0 + 2)² - 20 -> -12 = 4a - 20 -> 4a = 8 -> a = 2

Therefore, the equation of the parabola is: y = 2(x + 2)² - 20