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Published byRandell Thornton Modified over 6 years ago
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Investigating Characteristics of Quadratic Functions
Part 1
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What have we already seen?
We have seen equations in these forms. 1. y = x² 2. y = -3x² 3. y = -0.5x² + 4
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Some look like these and are trinomials.
y = x² + 2x + 1 y = -x² - 3x – 6 These are quadratic equations written in standard form. The standard form of a quadratic equation is y = ax² + bx + c
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Look at some characteristics
y = x² + 4x + 3 Y-intercept Vertex
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Let’s graph a couple of these and look at the vertex and y-intercept
y = x² + 2x + 1
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Another graph… y = x² + 2x + 6
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And Another… y = -3x² + 6x - 2
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Axis of Symmetry The axis of symmetry is the vertical line that passes through the vertex. Now go back to the graphs and draw in the axis of symmetry.
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How can we find the vertex of a quadratic function without graphing it?
From standard form y = ax² + bx + c y = x² + 2x Find 2. Plug that in for x in the equation to find y. 3. Be sure to write the vertex as an ordered pair (x, y).
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Try a few of these… Find the vertex. 1. y = 3x² + 6x - 2
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Now let’s look at the y-intercept
What is the y-intercept of a parabola? How do you find the y-intercept on a graph? How would you find the y-intercept of a parabola if you don’t graph it but you have the equation?
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More on the y-intercept
How would you find the y-intercept of a parabola if you don’t graph it but you have the equation? Example: y = x² + 2x + 3 1. Let x = 0 2. Plug 0 in everywhere there is an x and solve for y. 3. Be sure to write the y-intercept as an ordered pair (x, y).
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Try a few of these… Find the y-intercept 1. y = 4x² - x + 1
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