Standard Form, Factored Form, Vertex Form Name printable pdf download

Standard Form, Factored Form, Vertex Form Name

Standard Form, Factored Form, Vertex Form

Name: ______________________________

How are a quadratic’s factored form, x-intercepts, vertex, and vertex form related? Fill in the missing entries in the table below. (Show all

work on a separate sheet of paper, and keep it clearly labeled.)

Standard Form

Factored Form

x-intercepts

Vertex

Vertex Form

(1, 0) and (-5, 0)

(-2, 9)

(-2, 0) and (9, 0)

(3.5, -30.25)

(6, 0) and (-4, 0)

(1, -25)

(3, 0) and (-7, 0)

(-2, -25)

(-2, 0) and (6, 0)

(2, -16)

4, 0 and 6, 0

(1, -25)

(2, 0) and (-8, 0)

(-3, -25)

5, 0 and

(-3, 0)

1, 16

(5, 0) and (-5, 0)

(0, -25)

(3, 0)

Suppose you are given the x-coordinate of a point on a parabola. How can you find the corresponding y-coordinate?

You can substitute the x-coordinate in to the equation and solve for y.

How is a parabola’s factored form related to its x-intercepts?

When the parabola is in factored form, using the zero-product property I can set each factor equal to zero. The solutions to these equations

are the x-intercepts of the parabola.

How are the coordinates of a parabola’s vertex related to its x-intercepts?

If the parabola’s vertex is above the x-axis and the parabola is concave up, it will have 0 x-intercepts.

If the parabola’s vertex is above the x-axis and the parabola is concave down, it will have 2 x-intercepts.

If the parabola’s vertex is below the x-axis and the parabola is concave down, it will have 0 x-intercepts.

If the parabola’s vertex is below the x-axis and the parabola is concave up, it will have 2 x-intercepts.

If the parabola’s vertex is on the x-axis the parabola will have 1 x-intercept (the vertex) whether it is concave up or down.

Standard Form, Factored Form, Vertex Form Name