MATH SOLVE

4 months ago

Q:
# HELP ASAP FOR BRAINLIEST:What is the equation of a quadratic function with roots -1 and -7 and a vertex at (-4, 7)?Please show step by step how you did this, providing the original formula and then the formula with numbers added in. THANK YOU!

Accepted Solution

A:

Answer: y = -14/9(x + 4)^2 + 7Step-by-step explanation:The given roots of the quadratic function is (-1, -7)The vertex is at (-4, 7)The formula is y = a(x - h)^2 + kThe vertex is (h, k)Comparing with the given vertex, (-4, 7), h = -4 and k = 7Substituting into the formula y = a(x - h)^2 + k, it becomesy = a(x - - 4)^2 + 7 y = a(x + 4)^2 + 7From the roots given (-1, -7)x = -1 and y = -7Substituting x = -1 and y = -7 into the equation, y = a(x + 4)^2 + 7, it becomes-7 = a(-1+4)^2 + 7-7 = a(3^2 ) + 7- 7 = 9a + 7-7-7 = 9a9a = -14a = -14/9Substituting a = - 14/9 into the equation, it becomesy = -14/9(x + 4)^2 + 7