Find the equation of the quadratic function with the coordinates (-3,-2) (-2,-5)

Question

The question is listed above, thanks.

Answer 1

Hey! Lets solve this shall we ?

So, we must find the equation of a quadratic function given the two points (-3,-2) and (-2,-5). We notice that when we plot these points, (-2,-5) is the vertex of the parabola (Quadratic) passing through the point (-3,-2). Then, we must use the equation of a parabola

f(x) = a(x - h)² + k

to find our equation. Next, we plug in both points where (h,k) is the vertex and (x,y) is the point the graph is passing through to solve for a such that

-2 = a(-3 - (-2))² - 5..............Then we add 5 to the left side to obtain

3 = a(-1)²........(-1)² = 1. Then,

a = 3.

We can now plug in the a value to obtain our equation using the vertex such that

f(x) = 3(x + 2)² - 5

I hope this helped!