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13.2 Solving Quadratic Equations by Graphing CORD Math Mrs. Spitz Spring 2007
Objectives Identify standard form coefficients in a standard formula Determine how a parabola opens Find the coordinates of the vertex Sketch a graph of a function.
Assignment 9.3 Worksheet A and B
Identify the values of a, b, and c in the functions. Standard form of a quadratic function: ax 2 + bx + c a, b and c represent coeeficients in the function. a 0
Ex. 1: Identify the values of a, b, and c in the functions. y = -x 2 + 4x – 8 a = -1 b = 4 c = -8
Tell whether the graph opens up or down. Write the equation of the axis of symmetry. If a is positive, the parabola opens up. If a is negative, the parabola opens down.
Ex. 2: Tell whether the graph opens up or down and state the equation of the axis of symmetry. The parabola opens up because a is positive 7.
Find the coordinates of the vertex. In order to find the coordinates of the vertex, you must find the axis of symmetry, then plug in the value you find for x and determine the value for y.
Ex. 3 Find the coordinates of the vertex. Find the value for x using the formula for axis of symmetry.
Ex. 3 Find the coordinates of the vertex. Then substitute the value for x and solve for y. The vertex for this equation is at (1, 19).
Ex. 4: Find the coordinates of the vertex. Make a table of values using 2 x-values to the left and right of the vertex.
xy -37 -2 3 0 1
Ex. 4: Find the coordinates of the vertex. Make a table of values using 2 x-values to the left and right of the vertex. xy -37 -24 3 0 1
Ex. 4: Find the coordinates of the vertex. Make a table of values using 2 x-values to the left and right of the vertex. xy -37 -24 3 04 1
Ex. 4: Find the coordinates of the vertex. Make a table of values using 2 x-values to the left and right of the vertex. xy -37 -24 3 04 17 Next step is to graph the points.
xy -37 -24 3 04 17 vertex
Parabola Conic section.
If the leading coefficient of a quadratic equation is positive, then the graph opens upward. axis of symmetry f(x) = ax2 + bx + c Positive #
QUADTRATIC RELATIONS Standard Form.
1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.
Essential Question: How do you determine whether a quadratic function has a maximum or minimum and how do you find it?
You can use a quadratic polynomial to define a quadratic function A quadratic function is a type of nonlinear function that models certain situations.
Quadraticsparabola (u-shaped graph) y = ax2 y = -ax2 Sketching Quadratic Functions A.) Opens up or down: 1.) When "a" is positive, the graph curves upwards.
Section 4.1: Vertex Form LEARNING TARGET: I WILL GRAPH A PARABOLA USING VERTEX FORM.
Graphing Quadratics With VERTEX and Axis of Symmetry At the end of the period, you will learn: 1. To compare parabola by the coefficient 2. To find the.
10.1 Graphing Quadratic Functions p. 17. Quadratic Functions Definition: a function described by an equation of the form f(x) = ax 2 + bx + c, where a.
Warmup 9-11 Solve the following equations by factoring. Show work! 1.x x - 80 = 0 2.Solve by using the quadratic formula: 4x 2 - 5x - 2 = 0 3.Solve.
© Boardworks Ltd of 14 Graphs parabolas by calculating strategic points.
5.5 – The Quadratic formula Objectives: Use the quadratic formula to find real roots of quadratic equations. Use the roots of a quadratic equation to locate.
Graphing Quadratic Equations Standard Form & Vertex Form.
9.3 Graphing Quadratic Functions
Graphing Quadratic Equations
Chapter 10.1 Notes: Graph y = ax 2 + c Goal: You will graph simple quadratic functions.
Graphing Quadratic Functions
Graphing Quadratic Functions (2.1.1) October 1st, 2015.
Vertex & axis of Symmetry I can calculate vertex and axis of symmetry from an equation.
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