Algebra Chapter 10-1 Exploring Quadratic Graphs

Algebra Chapter 10-1Exploring Quadratic Graphs

Graphing Quadratic Functions NC SCOS 4.02 

Graph, factor, and evaluate quadratic functions to solve

problems.

What you’ll learn

New Vocabulary

Quadratic FunctionsA QUADRATIC FUNCTION will show up as a U-shaped graph called a PARABOLA.

The graph of a quadratic function is a U-shaped curve called a parabola. The graph of y = x2, shown at the right, is a parabola.

Examples of Parabolic Curves

steel cables of a suspension bridge

the supporting arches of some highway

railroad bridges, for it is this shape that naturally holds up a uniformly weighted road surface

A baseball in flight or the arc of water at the lip of a waterfall both follow a parabolic path.

You can fold a parabola so that the two sides match exactly. This property is called symmetry. The highest or lowest point of a parabola is its vertex, which is on the axis of symmetry.

The fold or line that divides the parabola into two matching halves is called the axis of symmetry.

Minimum or Maximum?

Quadratics Notes

The Coefficient and the U

Practice Problems from Text

Graphing the Quadratic Equation

Graphing CalculatorMath Bits –Parabolas- http://mathbits.com/MathBits/TISection/Algebra1/Parabolas.htm

Graphing By Hand

Create a table and graph three to four points.

x y

Online Resources

Video Tutor

Make a table of values and graph

y 2x2

Domain Range

2

1

0

1

2

If you graph a quadratic function on a piece of paper and fold it down the middle, the two sides will match exactly. The line down the middle of the parabola is called the AXIS OF SYMMETRY. The two symmetric parts are mirror images of each other. The VERTEX is the lowest point (minimum) of a parabola that opens up or the highest point (maximum) of a parabola that opens down.

Glossary of TermsQuadratic function (p. 510) A function of the form y = ax2 + bx + c, where a ≠ 0. The graph of a quadratic function is a parabola, a U-shaped curve that opens up or down.

Standard form of a quadratic function (p. 510) The form of a quadratic function written y = ax2 + bx + c, where a ≠ 0.

Parabola (p. 510) The graph of a quadratic function.

Axis of symmetry (p. 511) The line that divides a parabola into two matching halves.