Question

What is the standard form of the quadratic function that has a vertex at(-3,-5) and goes through the point (0, 13)?

Answer 1

Note that a quadratic function can be written in vertex form as:.....

`y=a(x-k)^2\text{ + h}`

Now, its vertex will be at (k,h)... where k = -3 and h = -5

`y=a(x+3)^2\text{ - 5}`

Since it passes through the point (0, 13), we have .....

`\begin{gathered} 13=a(0+3)^2\text{ -5} \\ 13\text{ = 9a - 5} \\ \text{13 + 5 = 9a} \\ a\text{ = }(18)/(9) \\ a\text{ = 2} \end{gathered}`

So, the standard form of the quadratic function is....

`\begin{gathered} y=2(x+3)^2\text{ - 5} \\ y\text{ = 2(x + 3)(x + 3) - 5} \\ y=2(x^2\text{ + 6x + 9) - 5} \\ y=2x^2\text{ + 12x + 18 - 5} \\ y=2x^2\text{ + 12x +13} \end{gathered}`