Quadratic Models: Important Facts: 1) Quadratic Equations ...
Section 7.1 Solving Quadratic Equations by Graphing...
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Section 7.1 Solving Quadratic Equations by Graphingsoln.notebook
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Unit 7: Quadratic Equations
Section 7.1 Solving Quadratic Equations by Graphing
Section 7.1 Solving Quadratic Equations by Graphingsoln.notebook
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What is a quadratic equation?
• Any equation in the form• The highest power (called the degree) is always 2
What is a quadratic function?
→ Any equation of the form or
The difference between a quadratic function and a quadratic equation is:
→ a quadratic equation is set equal to 0 or a constant.→ a quadratic function is set to equal f(x) or y
Quadratic Function:
Quadratic Equation:
Section 7.1 Solving Quadratic Equations by Graphingsoln.notebook
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Review of Quadratic Functions
For the function:
AOS:
Vertex and type:
yintercept:
xintercepts:
This unit we focus on a variety of methods on how to solve quadratic equations Ø graphingØ factoringØ using the quadratic formula.
is called a quadratic equation.
Section 7.1 Solving Quadratic Equations by Graphingsoln.notebook
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Quadratic Equations
Terminology
• Graphs have xintercepts • Quadratic functions have zeros • Quadratic equations have roots
→ Roots are solutions to any quadratic equation.→ The roots of a quadratic equation are equal to the xintercepts of the parabola→ The roots of a quadratic equation are equal to the zeros of the function f(x)
Section 7.1 Solving Quadratic Equations by Graphingsoln.notebook
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Example: Consider the function
a) What are the xintercepts?b) What are the zeros?c) What are the roots?d) Solve the function.
Section 7.1 Solving Quadratic Equations by Graphingsoln.notebook
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Method 1: Graphing
Example 1: Solve by graphing:
AOS
Vertex
Table of Values
Section 7.1 Solving Quadratic Equations by Graphingsoln.notebook
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The number of real roots or solutions a quadratic equation has in standard formax2 + bx + c = 0 is the number of times the corresponding parabola y = ax2 + bx + c intersects the xaxis.
The roots of a quadratic equation are the xintercepts of the graph of the corresponding function. There may be two, one or no solution.
Section 7.1 Solving Quadratic Equations by Graphingsoln.notebook
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Solving quadratics by graphing
1. Rearrange the equation so that all terms are on one side of the equation and the equation equals 0
2. Graph the corresponding function.3. The solutions are the xintercepts of the graph. Some solutions may need
to be estimated. (Graphing software such as desmos or gracalc can help you with this.)
Section 7.1 Solving Quadratic Equations by Graphingsoln.notebook
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Ex) Solve the following quadratic equations by graphing. Use graphing software but include sketches of your graphs.
1) x2 + 7x + 12 = 0
2) 4.9x2 + 19.2x + 5.2 = 0
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3) 2x2 12x = 18
4) 2x2 5x + 3 = 3x(2 x)
Section 7.1 Solving Quadratic Equations by Graphingsoln.notebook
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Example 3: The path of a football at one particular kickoff can be modelled using the function h(d) = 0.02d 2 + 2.6d 66.5 , where h is the height of the ball above the ground (yards) and d is the horizontal distance from the kicking team’s goal line (yards).
(a) What are the xintercepts? What do they mean in the context of the problem? Why are there two xintercepts?
(b) What horizontal distance does the ball travel before it hits the ground?
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