express the quadratic function in standard form given that it has the vertex (-1,-2) and passes through (3,30)

Question

express the quadratic function in standard form given that it has the vertex (-1,-2) and passes through (3,30)

Answer 1

The standard form equation for a quadratic function is given by

f(x) = a(x-h)² + k Where the vertex is the point (h,k)

The problem gives us the vertex as (-1,-2) so we know h = -1 and k = -2

f(x) = a(x+1)² - 2

Now we just need to find the value of a

We can use the point (3,30) since we know the function passes through this point

plug in x = 3 and f(x) = 30

30 = a(3+1)² - 2

30 = a(4)² -2

30 = 16*a - 2

32 = 16*a

a = 2

So our final equation is

f(x) = 2(x+1)² - 2