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.

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

From to , the average rate of change for both functions is negative

For the quadratic function, , the coordinate is a solution to the equation of the function

Step-by-step explanation:

we have the quadratic functions

Verify each statement

case A) The quadratic function, , 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 represent and x-intercept and a y-intercept

therefore

The statement is True

case B) The quadratic function, , has an x-intercept at the origin

The quadratic function, has no x-intercept

so

The statement is False

case C) From to , the average rate of change for both functions is positive

Observing the graph from to , the average rate of change for both functions is negative

so

The statement is False

case D) From to , the average rate of change for both functions is negative

The statement is True

case E) For the quadratic function, , the coordinate 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

------> is not true

The ordered pair is not a solution

so

The statement is False

case F) For the quadratic function, , the coordinate 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

------> is true

The ordered pair is a solution

so

The statement is True

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

answer: 486in^2

step-by-step explanation: