Section 4.1: Vertex FormLEARNING TARGET: I WILL GRAPH A PARABOLA USING VERTEX FORM.

VERTEX FORM

Vertex Form for a Parabola:

a = stretch or shrink of parabola; if a <1, there is a vertical shrink, if a > 1, there is a vertical stretch. If a is negative, the parabola is reflected in the line y = k (the value of k)

(h,k) = vertex of parabola

Recall Axis of Symmetry: in this case it will be x = h.

Example 1: Graph

Step 1: Determine the vertex, (h,k).

Step 2: Determine the axis of symmetry for the parabola.

Step 3: Determine if vertex is a maximum value or a minimum value.

Step 4: Create a table of values (at least 5 points including the vertex). Also, one point needs to have x-value of zero so you can determine y-intercept.

Step 5: Graph the parabola.

Example 2: Graph

Step 1: Determine the vertex, (h,k).

Step 2: Determine the axis of symmetry for the parabola.

Step 3: Determine if vertex is a maximum value or a minimum value.

Step 4: Create a table of values (at least 4 points including the vertex). Also, use an x value of zero to determine the y intercept.

Step 5: Graph the parabola.

Creating a Parabola in Vertex Form When a Vertex and a Point are Given

If you are given a vertex and a point on the graph, you can use this information to create an equation for the parabola.

Step 1: Substitute vertex value in .

Step 2: Substitute point into your function you created in step 1 (a will still be unknown).

Step 3: Solve for a.

Step 4: Substitute the a value you found, along with the vertex, into

and you have created your equation.

Example 3: Write the equation of the parabola in vertex form: vertex (-3,-4) point (-1,-8)

Step 1: Substitute vertex value in .

Step 2: Substitute point into your function you created in step 1 (a will still be unknown).

Step 3: Solve for a.

Step 4: Substitute the a value you found, along with the vertex, into

and you have created your equation.

Example 4: Write the equation of the parabola in vertex form: vertex(2,3) y intercept:11

Step 1: Substitute vertex value in .

Step 2: Substitute point into your function you created in step 1 (a will still be unknown).

Step 3: Solve for a.

Step 4: Substitute the a value you found, along with the vertex, into

and you have created your equation.

Assignment

Graphing a Parabola from Vertex Form Worksheet

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