9 4 Graphing Quadratics Three Forms A quadratic

�A quadratic equation can be written in three vertex different forms: form, standard form,

� The Vertex Form vertex form of a quadratic equation is: graph the function

Graph the parabola. 1. a. Find the vertex. b. Find the axis of symmetry.

Graph the parabola. 2. a. Find the vertex. b. Find the axis of symmetry.

Standard Form � The vertex form of a quadratic equation is: � The graph

Graph the parabola. 3. a. Find the vertex. b. Find the axis of symmetry.

Graph the parabola. 4. a. Find the vertex. b. Find the axis of symmetry.

Factored Form � The vertex form of a quadratic equation is: � The graph

Graph the parabola. 5. a. Find the vertex. b. Find the axis of symmetry.

Graph the parabola. 6. a. Find the vertex. b. Find the axis of symmetry.

Write the equation in vertex form. 7. The parabola has a vertex at and

Write the equation in vertex form. 8. The parabola has a = 2, had

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9. 4 Graphing Quadratics Three Forms

�A quadratic equation can be written in three vertex different forms: form, standard form, and factored form. � In order to graph each form, we need four key points and a key axis. The method to find these varies by form. � vertex � axis of symmetry � x-intercepts � y-intercept

� The Vertex Form vertex form of a quadratic equation is: graph the function is a parabola with vertex at. The parabola is symmetric with respect to the line. If , the parabola opens upward ; if , the parabola downward opens.

Graph the parabola. 1. a. Find the vertex. b. Find the axis of symmetry. c. Find the x-intercepts (let y=0) d. Find the y-intercept (let x=0)

Graph the parabola. 2. a. Find the vertex. b. Find the axis of symmetry. c. Find the x-intercepts (let y=0) d. Find the y-intercept (let x=0)

Standard Form � The vertex form of a quadratic equation is: � The graph the function is a parabola with vertex at. The parabola is symmetric with respect to the line. If ; if upward opens downward , the parabola opens , the parabola.

Graph the parabola. 3. a. Find the vertex. b. Find the axis of symmetry. c. Find the x-intercepts (let y=0) d. Find the y-intercept (let x=0)

Graph the parabola. 4. a. Find the vertex. b. Find the axis of symmetry. c. Find the x-intercepts (let y=0) d. Find the y-intercept (let x=0)

Factored Form � The vertex form of a quadratic equation is: � The graph the function is a parabola with vertex at. The parabola is symmetric with respect to the line. If ; if upward opens downward , the parabola opens , the parabola.

Graph the parabola. 5. a. Find the vertex. b. Find the axis of symmetry. c. Find the x-intercepts (let y=0) d. Find the y-intercept (let x=0)

Graph the parabola. 6. a. Find the vertex. b. Find the axis of symmetry. c. Find the x-intercepts (let y=0) d. Find the y-intercept (let x=0)

Write the equation in vertex form. 7. The parabola has a vertex at and passes through the point

Write the equation in vertex form. 8. The parabola has a = 2, had x = -3 as its axis of symmetry, and passes through the point