Write the quadratic function in the form

Question

Write the quadratic function in the form f(x)=a(x-h)²+k

.Then, give the vertex of its graph.

f(x)=2x²+20x+48

Answer 1

Looking at the desired form, you know immediately that a = 2 (because this is what multiplies x^2). So, first factor out a 2 from the equation:

f(x) = 2(x^2+10x+24).

Now, look at the part in the (). What do I add twice to get 10? The answer is 5. So far,

f(x) = 2((x+5)^2+24-25).

Why do we need to subtract 25?

Finally, distribute to get the final result:

f(x) = 2(x+5)^2 - 2.