Use the quadratic equation y = x^2 - 20x + 32 to answer the following questions

Question

1. How do you find the zeros of the function?
2. What are the zeros of the function?
3. How do you find the axis of symmetry?
4. What is the axis of symmetry of the function?
5. How do you use the axis of symmetry to find the vertex?
6. What is the vertex of the function?

Answer 1

Use the quadratic formula to get the zeros.

The axis of symmetry for the usual quadratic (Ax² + Bx + C = 0) occurs where x = -B/2A.

Put the abscissa (x value) of the axis of symmetry into the quadratic expression to get the ordinate (y value) of the vertex.

You can also get some of this information by converting to the vertex form which requires completing the square...which will also allow you to get the roots (zeros).

Answer 2

Hello Kelton,

1) How do you find the zeros of the function?

The zeros of the equation are also the x intercept. To find the x intercepts we need to use the quadratic formula: x = [-b ± sqrt(b^2-4ac)]/2a]

2)

For y = x^2 - 20x + 32

a= 1

b=-20

c=32

Plugging these values in we get:

x = -10 ± 2*sqrt{17}

3) For a function to the second power (like this function) the axis of symmetry is the vertical line passing through the vertex. We can find the x coordinate of the vertex with this equation:

x=-b/2a

4) Plugging in our numbers we find that the line of symmetry is x = 10

5) We already found the x coordinate of the vertex with the equation above so we just have to plug 10 into y = x^2 - 20x + 32 to find what y equals.

6)

y= 10^2 - 20*10+32

=100 - 200 + 32

=-132