Question

Complete the square for the following quadratic function:

y = -6x2 + 36x - 12

Then, graph the function. Point out the line of symmetry and state the maximum or minimum value.

Answer 1

y = -6x^2 + 36x - 12

y = -6(x^2 - 6x) - 12

y =  -6[ (x - 3)^2 - 9] - 12

y =  -6(x - 3)^2 + 54 - 12

y = -6(x - 3)^2 + 42

the vertex is at x = 3  so line of symmetry is x = 3

it will have a maximum value of 42  (as the vertex is at (3,42)

Answer 2

Answer:

Line of symmetry x = 3

Maximum of the parabola is 42.

Step-by-step explanation:

The given equation is of a quadratic function y = -6x² + 36 x - 12

Now we will convert this equation in the vertex form to get the the maximum value.

y = -6(x²- 6x + 2 + 9 - 9)

y = -6[(x² - 6x + 9) -7]

y = -6[(x - 3)² - 7]

y = -6(x - 3)² + 42

Vertex of the given parabola will be (3, 42) and the maximum value is 42.

Since coefficient is negative so opening of the parabola is downwards.

Line of symmetry is x = 3.