4.a graph quadratic equations warm-up
TRANSCRIPT
4.a Graph Quadratic Functions [4.1, 4.2].notebook
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Warm-up• Graph the following equations by finishing the
table.
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4.a Graph Quadratic Equations [4.1,4.2]
After this lesson you will be able to…
• Use a quadratic equation to find the vertex, axis of symmetry, direction of opening, and dilation and shape.
• Translate an equation in standard form to vertex form.
• Write an equation in vertex form from a given graph of a quadratic
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A quadratic function is a function described by an equation that can be written in the form
f(x)= ax2 + bx + c
A quadratic term is the term ax2 in the quadratic function
A linear term is the term bx in the quadratic function
A constant term is the term c in the quadratic function
Quadratic Functions
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Quadratic Functions and Their Graphs
• When graphed, quadratic functions create a parabola.
• A parabola is a U shaped graph.
• A parabola looks like
• The parent graph of a parabola is y=x2
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Let’s explore• Graph y=x2
• Let’s try adding and subtracting numbers…
• What do you notice?
> If we add a number, the graph shifts _____.
> If we subtract a number, the graph shifts ________
• Let’s try adding and subtracting numbers inside the square (y= (x ± #)2)…
• What do you notice?
> If we add a number, the graph moves to the _______
> If we subtract a number, the graph moves to the ________
• What happens if we make the x2 negative?> The graph _______ upside down
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BIG IDEA!!!Graph of any parabola can be written in the form
y = a(x - h)2 + k
• if h>0, the graph moves right |h| units
• If h<0, the graph moves to the left |h| units
• If k>0, the graph moves up |k| units
• If k<0, the graph moves down |k| units
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What do all these letters mean???
• Y is the y-coordinate
• A is the coefficient which dilates the graphs
> makes it wider or thinner
• X is the x-coordinate
• H is the number that shifts the graph right or left
> does not change the shape of the graph
• K is the number that shifts the graph up or down
> Does not change the shape of the graph
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Characteristics about the Graph
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Example 1:
• Use the equation to find the (1)vertex, (2) axis of symmetry, (3) direction of opening, (4) dilation and shape (5) Domain and Range(. Then Graph!
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Example 2:• Use the equation to find the (1)vertex, (2) axis of
symmetry, (3) direction of opening, (4) dilation and shape (5) Domain and Range. Then Graph!
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Example 3:• Use the equation to find the (1)vertex, (2) axis of
symmetry, (3) direction of opening, (4) dilation and shape (5) Domain and Range. Then Graph!
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Example 4:• Use the equation to find the (1)vertex, (2) axis of
symmetry, (3) direction of opening, (4) dilation and shape (5) Domain and Range. Then Graph!
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Practice• Find the vertex, axis of symmetry, direction of opening,
dilation, domain and range of the following. Then graph!
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Another way to find the Vertex …
• When the equation is NOT given to you in the form y = a(x - h)2 + k, it will be in this form..
y = ax2 + bx + c
• Use this to find the vertex….
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Let’s Practice
• Find the vertex of the following equations.
5) y = x2 + 8x + 71
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Let’s Practice
• Find the vertex of the following equations.
6) y = 3x2 – 6x – 5
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You Try…
• Find the vertex of the following equations.
7) y = x2 + 16x + 71
HINT use the equation
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You Try…
• Find the vertex of the following equations.
8) y = x2 – 2x – 5
HINT use the equation
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Example 9• Create the equation in vertex form which would graph the
given normal shaped (no dilation) parabola. State the Domain and Range of the function in interval notation.
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Example 10• Create the equation in vertex form which would graph the
given normal shaped (no dilation) parabola. State the Domain and Range of the function in interval notation.
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Example 11• Create the equation in vertex form which would graph
the given normal shaped (no dilation) parabola. State the Domain and Range of the function in interval notation.
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Example 12• Create the equation in vertex form which would graph the
given normal shaped (no dilation) parabola. State the Domain and Range of the function in interval notation.
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Example 13• Create the equation in vertex form which would graph the
given normal shaped (no dilation) parabola. State the Domain and Range of the function in interval notation.
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Homework:• ST 4.a both sides
• Checkpoint Tomorrow!
• Chapter 4 Test will be Tuesday 3/18!
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