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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
#13 is bonus