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Determine which situations best represent the scenario shown in the graph of the quadratic functions, y = x2 and y = x2 + 3. Select all that apply.

The quadratic function, y = x2, has an x-intercept at the origin

The quadratic function, y = x2 + 3, has an x-intercept at the origin

From x = -2 to x = 0, the average rate of change for both functions is positive

From x = -2 to x = 0, the average rate of change for both functions is negative

For the quadratic function, y = x2, the coordinate (2, 3) is a solution to the equation of the function.

For the quadratic function, y = x2 + 3, the coordinate (2, 7) is a solution to the equation of the function.

Determine which situations best represent the scenario shown in the graph of the quadratic functions y x2 and y x2 3 Select all that apply The quadratic functio class=

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MissPhiladelphia
The best represent the scenario shown in the graph of the quadratic functions, y = x2 and y = x2 + 3 are the following:  
The quadratic function, y = x2, has an x-intercept at the origin  

From x = -2 to x = 0, the average rate of change for both functions is negative  

For the quadratic function, y = x2 + 3, the coordinate (2, 7) is a solution to the equation of the function.  
calculista

Answer:

The quadratic function, [tex]y=x^{2}[/tex], has an x-intercept at the origin

From [tex]x = -2[/tex] to [tex]x = 0[/tex], the average rate of change for both functions is negative

For the quadratic function, [tex]y=x^{2}+3[/tex], the coordinate [tex](2, 7)[/tex] is a solution to the equation of the function

Step-by-step explanation:

we have the quadratic functions

[tex]y=x^{2}[/tex]

[tex]y=x^{2}+3[/tex]

Verify each statement

case A) The quadratic function, [tex]y=x^{2}[/tex], has an x-intercept at the origin

Remember that

The x-intercept is the value of x when the value of y is equal to zero

The point [tex](0,0)[/tex] represent and x-intercept and a y-intercept

therefore

The statement is True

case B) The quadratic function, [tex]y=x^{2}+3[/tex], has an x-intercept at the origin

The quadratic function, [tex]y=x^{2}+3[/tex] has no x-intercept

so

The statement is False

case C) From [tex]x = -2[/tex] to [tex]x = 0[/tex], the average rate of change for both functions is positive

Observing the graph from [tex]x = -2[/tex] to [tex]x = 0[/tex], the average rate of change for both functions is negative

so

The statement is False

case D) From [tex]x = -2[/tex] to [tex]x = 0[/tex], the average rate of change for both functions is negative

The statement is True

case E) For the quadratic function, [tex]y=x^{2}[/tex], the coordinate [tex](2, 3)[/tex] is a solution to the equation of the function

we know that

If a ordered pair is a solution of the quadratic function

then

the ordered pair must be satisfy the quadratic equation

Substitute the value of x and the value of y in the quadratic function and then compare

[tex]3=2^{2}[/tex]

[tex]3=4[/tex] ------> is not true

The ordered pair is not a solution

so

The statement is False

case F) For the quadratic function, [tex]y=x^{2}+3[/tex], the coordinate [tex](2, 7)[/tex] is a solution to the equation of the function

we know that

If a ordered pair is a solution of the quadratic function

then

the ordered pair must be satisfy the quadratic equation

Substitute the value of x and the value of y in the quadratic function and then compare

[tex]7=2^{2}+3[/tex]

[tex]7=7[/tex] ------> is true

The ordered pair is a solution

so

The statement is True

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