Question

Need help writing a quadratic equation from a function given the graph, screenshot posted of the question

Answer 1

g(x) = -x² + 10x - 30

the equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here vertex = (5, - 5 ), hence

y = a(x - 5)² - 5

to find a substitute the point on the graph (8, - 14) into the equation

- 14 = 9a - 5 ⇒ 9a = - 9 ⇒ a = - 1

y = - (x - 5)² - 5 = - (x² - 10x + 25) - 5 = - x² + 10x - 30

g(x) = - x² + 10x - 30 ← in standard form