Question

Put the quadratic into the vertex and state the coordinates of the vertex. y=x²+20x+36?

Answer 1

The quadratic equation y=x²+20x+36 can be put into vertex form by completing the square, resulting in y=(x+10)²-64. The coordinates of the vertex are (-10, -64).

Step-by-step explanation:

To put the quadratic equation y=x²+20x+36 into vertex form, we need to complete the square. First, we factor out the leading coefficient (which is 1 in this case, so it's not needed).

Then we find the perfect square trinomial that the quadratic part of the expression creates. In this case, we need to take half of the 'b' term (which is 20), square it, and add and subtract this number inside the parentheses. Half of 20 is 10, and 10 squared is 100.

So the equation becomes:

y = (x + 10)² - 100 + 36

Which simplifies to:

y = (x + 10)² - 64

The equation is now in vertex form, which is y = a(x - h)² + k, where (h, k) is the vertex. Comparing this to our equation, the vertex is (-10, -64).