write a quadratic function whose graph has a vertex of (-4,-1) and passes through the point (0,15)

Question

i also need the work and the equation

Answer 1

Hello,

Recall that offsetting an equation in the x and y direction is a matter of modifying the base x and y values:

y = x² is our basic formula

y = (x-a)² + b is the modified form, with (a,b) being the point of the vertex.

In order to also get the formula to hit the desired point, we need an additional scaling parameter c that multiplies by the original (x-a)²

y = c*(x-a)² + b is the final modular formula

now just plug in a and b from your vertex point (a = -4, b = -1) and c is solved for by then plugging in the point (0,15) into x and y as follows:

y = c*(x+4)² - 1

now with x = 0 and y = 15

15 = c*(0+4)² - 1

15 = c*(16) - 1

16 = 16*c

c = 1

so the final equation is:

y = (x+4)² - 1

You can test this, as plugging in x = 0 and y = 15 yields

15 = (16) - 1

15=15