50 points!!
The team wants to explore how it can change the steepness of the curved pit.
Identify how the graph of each equation compares with the graph of the parent quadratic equation, y = x^2.
Drag the equations to the correct location on the chart. Not all equations will be used.

Step-by-step explanation:

The graph of y = ax^2 + bx + c

A nonlinear function that can be written on the standard form

ax2+bx+c,wherea≠0

is called a quadratic function.

All quadratic functions has a U-shaped graph called a parabola. The parent quadratic function is

y=x2

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The lowest or the highest point on a parabola is called the vertex. The vertex has the x-coordinate

x=−b2a

The y-coordinate of the vertex is the maximum or minimum value of the function.

a > 0                   parabola opens up                    minimum value

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a < 0                    parabola opens down              maximum value

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A rule of thumb reminds us that when we have a positive symbol before x2 we get a happy expression on the graph and a negative symbol renders a sad expression.

The vertical line that passes through the vertex and divides the parabola in two is called the axis of symmetry. The axis of symmetry has the equation

x=−b2a

The y-intercept of the equation is c.

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When you want to graph a quadratic function you begin by making a table of values for some values of your function and then plot those values in a coordinate plane and draw a smooth curve through the points.

Example

Graph

x=x2+2x+1

Make a table of value for some values of x. Use both positive and negative values!

xy = x2 + 2x + 1

-34

-21

-10

01

14

29

316

Graph the points and draw a smooth line through the points and extend it in both directions

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Notice that we have a minimum point which was indicated by a positive a value (a = 1). The vertex has the coordinates (-1, 0)  which is what you will get if you use the formula for the x-coordinate of the vertex

x=−b2a=−22⋅1=−1

and that the line has an y-intercept of (0, 1) which could have been determined from the c-value which is 1.

If you have an absolute value of a that is greater than 1 the parabola will be narrower than the parental quadratic function. And the opposite that if you have a absolute value of a that is less than 1 then the parabola will be wider than the parental quadratic function.

If you have an absolute value of a that is greater than 1 the parabola will be narrower than the parental quadratic function. And the opposite that if you have a absolute value of a that is less than 1 then the parabola will be wider than the parental quadratic function.

step-by-step explanation: