Graphing Quadratic Functions Math 8A & Math 8AA 2017

What is the graph of the parent function of a quadratic function? The parent function of a quadratic function is in the form: Here’s the graph of the parent function: We call this shape a parabola. It can open up or down.

Parts of quadratic functions Y-intercept Zeros, AKA Roots

Terms to know Vertex: The “turn-around” point on the graph. When it is the top of the graph, it is called a MAXIMUM. When it is the bottom of the graph, it is called a MINIMUM. ZEROES, also called ROOTS, SOLUTIONS, X-INTERCEPTS: These are the points where the graph of a quadratic function crosses the x-axis. There may be 0, 1, or 2 of these for each function.

MORE terms to know Y-Intercept: This is the point where the graph crosses the y-axis. Axis of Symmetry: This is the vertical line through the x-coordinate of the vertex about which the parabola has horizontal symmetry. YOU MUST ALWAYS WRITE THIS AS A LINE, not a number: x=2; or x=0; or x=9, etc.

Forms of equations The STANDARD FORM is A, B, and C are numbers. They can be integers or rational numbers. The sign of A determines the direction the parabola opens. Positive – opens up; Negative – opens down

How do I find the vertex of a parabola? To find the x-coordinate of the vertex, use this formula: For example: The x-coordinate of the vertex for this equation is 1.

How do I find the vertex of a parabola? continued! To find the y-coordinate of the vertex, plug the x-coordinate into the equation and solve for y. For this example the vertex is (1, -5).

Axis of Symmetry The axis of symmetry is a vertical line, so it will always be in the form of x = ____. For the previous example, the vertex was (1, -5). The axis of symmetry is x = 1.

Graphing quadratics For this class, you will need to graph a quadratic by finding the vertex, axis of symmetry, and 2 points on either side of the vertex. Make a t-chart and write the vertex in the middle. From the previous example: x y 1 -5

Graphing quadratics Finish by filling in the remaining spaces in the chart by picking x-values and plugging them into the equation: x y -1 19 1 -5 2 3

Graphing quadratics Finish by plotting the points on a graph and connecting the dots. Draw in the Axis of Symmetry (AoS) as a dotted line. This graph is enlarged on the next slide.

Enlarged graph

Let’s try another one

Find the vertex and the axis of symmetry The x-coordinate = The y-coordinate = Vertex (2, 3); Axis of Symmetry: x=2 This parabola will open DOWN because the leading coefficient is negative.

Find the points needed to graph the function This is what your table looks like to start x y 2 3 x y -1 1 2 3 4 Final Table

Graph the function