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**Quadratic Functions and Their Graphs**

Lesson 1-7 Quadratic Functions and Their Graphs

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Objective:

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**To define and graph quadratic functions.**

Objective: To define and graph quadratic functions.

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Quadratic Function:

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Quadratic Function: f(x) = ax2 + bx +c where a 0.

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**The graph of a quadratic function is called a parabola.**

f(x) = ax2 + bx +c where a 0. The graph of a quadratic function is called a parabola.

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**Special Parts of a Parabola:**

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**Special Parts of a Parabola:**

Vertex: The turning point. It is either a maximum or minimum.

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**Special Parts of a Parabola:**

Axis of Symmetry: A vertical line that passes through the vertex.

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**Special Parts of a Parabola:**

Axis of Symmetry: This line is midway between the x-intercepts therefore it is the “average” of the x-values.

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Axis of Symmetry:

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**Can always be found by calculating the formula**

Axis of Symmetry: Can always be found by calculating the formula

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Vertex:

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**Can always be found using the formula**

Vertex: Can always be found using the formula

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Discriminant:

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**Discriminant: If b2 – 4ac > 0**

Parabola crosses x-axis twice. There will be two x-intercepts.

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**Discriminant: If b2 – 4ac > 0**

Parabola crosses x-axis twice. There will be two x-intercepts. If b2 – 4ac = 0 Parabola is tangent to the x-axis. There is only one x-intercept.

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**Discriminant: If b2 – 4ac > 0**

Parabola crosses x-axis twice. There will be two x-intercepts. If b2 – 4ac = 0 Parabola is tangent to the x-axis. There is only one x-intercept. If b2 – 4ac < 0 Parabola never crosses the x-axis so there are no x-intercepts.

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**Find the intercepts, axis of symmetry, and the vertex of the given parabola. y = (x + 4)(2x – 3)**

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Now sketch the graph.

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**Sketch the graph of the parabola**

Sketch the graph of the parabola. Label the intercepts, the axis of symmetry, and the vertex. y = 2x2 – 8x + 5

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**If the equation can be written in the form of :**

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**If the equation can be written in the form of :**

then the vertex of the parabola is (h, k) and the axis of symmetry is the equation x = h.

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**Find the vertex of the parabola by completing the square**

Find the vertex of the parabola by completing the square. y = -2x2 + 12x + 4

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**Now, find the x- and y-intercepts. y = -2x2 + 12x + 4**

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Find the equation of the quadratic function f with f(-1) = -7 and a maximum value f(2) = -1. Show that the function has no x-intercepts.

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**Where does the line y = 2x + 5 intersect the parabola y = 8 – x2**

Where does the line y = 2x + 5 intersect the parabola y = 8 – x2? *Show this both algebraically and graphically.

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Find an equation of the function whose graph is a parabola with x-intercepts 1 and 4 and a y-intercept of -8.

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**General Linear Function:**

So far we know f(x) = dx + e but we also know y = mx + b where m = slope.

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**What is the slope of y = ¼ x - 3?**

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**Assignment: Pgs. 40-41 C.E. 1-6 all W.E. 1-25 (Left Column)**

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