Section 5.1 – Graphing Quadratics

REVIEW

Graphing

Big Question…

Are lines the only type of graph?

Hhhmmm…what would Lisa say?

I GOT IT!

Some other types…

Have you seen these before?

Going a little farther…

What else could graphs look like?

Graphing a curve..

Is it possible that the certain equations when graphed will give us a curve?

YES Is it possible that other certain equations

give us neither a straight line or a curve, but something else totally different?

YES

Section 5.1 – Graphing a Quadratic EquationQuadratic Equation: trinomial function defined by the form y = ax2 + bx + c.

Examples: y = x2 + 4x + 5

y = 9x2 + 16x

y = - 4x2 - 11

Section 5.1 – Graphing a Quadratic EquationThree Parts of a Quadratic Equation:

y = ax2 + bx + c

Lead Coefficient Linear Coefficient

ConstantQuadratic Term

Linear Term

Section 5.1 – Graphing a Quadratic EquationParabola: graph of any quadratic term, which is a smooth continuous curve. (Shaped like a "U")

Vertex: Point on the parabola where the curve and axis of symmetry intersect. Also the local maximum and local minimum of the graph as well. Point where the direction of graph changes.

Section 5.1 – Graphing a Quadratic EquationAxis of Symmetry: Center line of a parabola, splits the parabola into two symmetrical halves.

Section 5.1 – Graphing a Quadratic EquationZeros of a Function: points (coordinates) where the curve intersects the x-axis.

Roots of a Quadratic Function: values of the variable that satisfy the quadratic equation.

Section 5.1 – Graphing a Quadratic EquationBase Quadratic

Function

y = x2

Vertex

Axis of Symmetry

Section 5.1 – Graphing a Quadratic EquationDomain of Base Quadratic Function:

ALL REAL NUMBERS

Range of Base Quadratic Function:

{ y | y > 0 }