# Quadratics Project

by
**aarthur**

Last updated 6 years ago

** Discipline: **

Math ** Subject: **

Algebra I
** Grade:**

7

Quadratics Project

1st Equation

2nd Equation

y=-x^2+2x-1

y=2x^2-2

Vertex=(0, -2)(How to find the vertex by hand is by doing a two step process. The first thing you do is find your AOS (formula shown above). This will be your x value (In this situation your x value is 0). Next substitute your AOS for the x and evaluate it out to get your y value (In this case it is -2). Put these together and you will have your coordinates. This is (0, -2).Axis of Symmetry=0(how to find the AOS in the equation is by solving the equation -(0)/2(2), which is 0.Solutions=-1, 1(How you find the solutions to a quadratic equation is by factoring. There are multiple steps to factoring. The first thing you do is multiply your a value and c value. Then find two numbers that multiply to that but add to your b value. Next you put your a value and one of the values that adds to b and multiplys to a.c. in parentheses, as well as the other value, besides the first one in parenthesis with the c value. GCF these values out. Then put the two factors in parenthesis and the common inside equation in parenthesis beside it. Lastly value it out so you get an equation of x=# with the two parenthesis. These are your two solutions or x intercepts.)Y-intercept=(0, -2)Domain=all real numbersRange= -2

Vertex-(1, 0)(How to find the vertex by hand is by doing a two step process. The first thing you do is find your AOS (formula shown above). This will be your x value (In this situation your x value is 1). Next substitute your AOS for the x and evaluate it out to get your y value (In this case it is 0). Put these together and you will have your coordinates. This is (1, 0).)Axis of Symmetry-1(how to find this AOS is by solving the equation-(2)/2(-1), which is 1.)Solutions-1(How you find the solutions to a quadratic equation is by factoring. There are multiple steps to factoring. The first thing you do is multiply your a value and c value. Then find two numbers that multiply to that but add to your b value. Next you put your a value and one of the values that adds to b and multiplys to a.c. in parentheses, as well as the other value, besides the first one in parenthesis with the c value. GCF these values out. Then put the two factors in parenthesis and the common inside equation in parenthesis beside it. Lastly value it out so you get an equation of x=# with the two parenthesis. These are your two solutions or x intercepts.)Y-Intercept- (0,-1)Domain-all real numbersRange- -1

their graphs

This rollercoaster is an example of a real life parabola. It is an example because it is a symmetrical curve being "U" shaped.

When a graph opens upward, like this, it means the "a" value is positive (this is a minimum graph)

When a graph opens downward like this, it means the "a" value is negative (this is a maximum graph)

How you can find the Axis of Symmetry by hand is by using the formula -b/2a

Need to know

the formula for a quadratic equation is ax^2+bx+c

Maximum Graph- Graph is opening downward, the a value is negative, and it looks like a upside down "u"

Minimum Graph- Graph is opening upward, the a value is positive, and it looks like a "u"

The Domain will always be all real numbers in parabolas because they go on forever.

2x^2-2 x l y -1 l 0 0 l -2 1 l 0 2 l 6 3 l 16

x^2+2x-1 x l y -1 l -4 0 l -1 1 l 0 2 l -1 3 l -4

their tables

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