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Algebra

9.3 & 9.4 Notes

Solving & Graphing Quadratic Functions

Homework: 9.3/9.4 Worksheet Day 1

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Standards:

A1.8.1 Graph quadratic, cubic, and radical equations.

A1.8.7 Use quadratic equations to solve word problems.

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9.3 Vocabulary

1. A quadratic function is a function that can be written in the standard form:

y = ax² + bx + c, where a ≠ 0

2. Every quadratic function has a U-shaped graph called a __________________________.

3. If the leading coefficient a is positive, the parabola ______________________________.

4. If the leading coefficient a is negative, the parabola _____________________________.

5. The _______________ is the lowest point of a parabola that opens up and the highest

point of a parabola that opens down.

6. The line passing through the vertex that divides the parabola into two symmetric parts is

called the ____________________________________________.

7. Solutions of quadratic functions can also be called the ______________________,

_______________________, or _______________________.

To find the Vertex and Axis of Symmetry

1. Put the quadratic function in standard form: y = ax² + bx + c

2. Identify the numeric values of a, b, and c.

3. The vertex has an x-coordinate of x =

a

b

2

. Plug in the values for a and b.

4. Substitute whatever you get for x in step 3 into the quadratic function to find

the y-coordinate of the vertex.

5. The axis of symmetry is the vertical line x =

a

b

2

Algebra

9.3 & 9.4 Notes

Solving & Graphing Quadratic Functions

Homework: 9.3/9.4 Worksheet Day 1

Example 1 – Find the vertex and Axis of Symmetry for these quadratic functions:

a.) y = -2x² + 4x – 9

a = ___ b = ___ c = ___

Vertex: __________

Axis of Symmetry: __________

b.) y = x² - 10

a = ___ b = ___ c = ___

Vertex: __________

Axis of Symmetry: __________

c.) y = x² + 4x – 1

a = ___ b = ___ c = ___

Vertex: __________

Axis of Symmetry: __________

d.) y = -2x² + 8x – 8

a = ___ b = ___ c = ___

Vertex: __________

Axis of Symmetry: __________

Steps for Graphing a Quadratic Function

1. Follow the above steps to find the vertex and axis of symmetry.

2. Plot the vertex and the axis of symmetry on a coordinate plane.

3. Make a table of values, using x-values to the left and right of the vertex.

4. Plot the points and connect them with a smooth curve to form a parabola.

Algebra

9.3 & 9.4 Notes

Solving & Graphing Quadratic Functions

Homework: 9.3/9.4 Worksheet Day 1

Example 2 – Graphing a Quadratic Function with a Positive a-value

a.) Sketch the graph of y = x² – 1 a = _____ b = _____ c = _____

Vertex: __________

AOS: __________

Roots: __________

Opens: __________

x

y

b.) Sketch the graph of y = -x² + 4x - 4 a = _____ b = _____ c = _____

Vertex: __________

AOS: __________

Roots: __________

Opens: __________

x

y

Algebra

9.3 & 9.4 Notes

Solving & Graphing Quadratic Functions

Homework: 9.3/9.4 Worksheet Day 1

c.) Sketch the graph of y = x² + 3 a = _____ b = _____ c = _____

Vertex: __________

AOS: __________

Roots: __________

Opens: __________

x

y

d.) Sketch the graph of y = 2x² + 8x a = _____ b = _____ c = _____

Vertex: __________

AOS: __________

Roots: __________

Opens: __________

x

y