Objective 2 - Graphing quadratic functions.

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Describe the salient characteristics of quadratic functions.

Link to section in online textbook.

First, watch the video below to learn what quadratic functions look like. You can use the notes here to follow along with the video and record your thoughts.

Now practice working with converting between quadratic equations and their graphs below.

Write the equation of the graph presented below in the form $f(x)=ax^2+bx+c$ , assuming $a=1$ or $a=-1$ .

$y = \answer {-1} x^2 + \answer {-2} x + \answer {2}$

Write the equation of the graph presented below in the form $f(x)=ax^2+bx+c$ , assuming $a=1$ or $a=-1$ .

$y = \answer {1} x^2 + \answer {2} x + \answer {-4}$

Write the equation of the graph presented below in the form $f(x)=ax^2+bx+c$ , assuming $a=1$ or $a=-1$ .

$y = \answer {1} x^2 + \answer {-2} x + \answer {2}$

Graph the equation $f(x)= (x-3)^2-19.$



	Choice A



	Choice B



	Choice C



	Choice D



	Choice E

A B C D E

Since Xronos does not like making dynamic graphs, we can’t practice questions like we could see on the exam perfectly. The questions below will do similar things you could see on the exam that you can practice.

Given the quadratic function has the vertex at $(\sage {vertex1[0]}, \sage {vertex1[1]})$ and is pointing up, construct the equation of the function. Assume $a=1$ or $a=-1$ .

$f(x) = \answer {\sage {equationCoefficients1[0]}}x^2 + \answer {\sage {equationCoefficients1[1]}}x + \answer {\sage {equationCoefficients1[2]}}$

To get started, write the equation in vertex form. Then, be careful as you multiply out.

Given the quadratic function has the vertex at $(\sage {vertex1[0]}, \sage {vertex1[1]})$ and is pointing up, construct the equation of the function. Assume $a=1$ or $a=-1$ .

$f(x) = \answer {\sage {equationCoefficients1[0]}}x^2 + \answer {\sage {equationCoefficients1[1]}}x + \answer {\sage {equationCoefficients1[2]}}$

To get started, write the equation in vertex form. Then, be careful as you multiply out.

Given the quadratic function has the vertex at $(\sage {vertex2[0]}, \sage {vertex2[1]})$ and is pointing down, construct the equation of the function. Assume $a=1$ or $a=-1$ .

$f(x) = \answer {\sage {equationCoefficients2[0]}}x^2 + \answer {\sage {equationCoefficients2[1]}}x + \answer {\sage {equationCoefficients2[2]}}$

To get started, write the equation in vertex form. Then, be careful as you multiply out.

Given the quadratic function has the vertex at $(\sage {vertex3[0]}, \sage {vertex3[1]})$ and goes through the point $(\sage {extraPoint3[0]}, \sage {extraPoint3[1]})$ , construct the equation of the function. Do not assume anything about $a$ .

$f(x) = \answer {\sage {equationCoefficients3[0]}}x^2 + \answer {\sage {equationCoefficients3[1]}}x + \answer {\sage {equationCoefficients3[2]}}$

To get started, write the equation in vertex form. We don’t know what $a$ is, but could we do something with the other given point to find $a$ ? Think about what you did in the linear functions Module...

If you still don’t know what to do, watch this short video.