An expression is shown below: f(x) = −25x2 + 30x − 9 part a: how many x-intercepts could the graph of f(x) have and what component of the polynomial indicates the potential x intercepts? what are the values of the x intercepts ? find the x intercepts by factoring and show all work. (4 points) part b: what is the value of the y-intercept of the graph of f(x) and what component of the polynomial indicates this value? (2 points) part c: discuss the end behavior of the graph of f(x) and what components of the polynomial indicate this behavior. (4 points)

See below.

Step-by-step explanation:

f(x) = -25x2 + 30x − 9

This is a parabola which opens downwards.

Part A.

The discriminant b^2 - 4ac = 30^2 - 4*(-25) * -9

= 900 - 900

= 0

This indicates that the graph of the function just touches the x-axis. So there is one root of multiplicity 2.

Factoring:

-25x2 + 30x − 9

=  -(25x^2 - 30x + 9)

= -(5x - 3)(5x - 3)

so the roots are x = 3/5  multiplicity 2.

The x -intercept is at (0.6, 0).

Part B.

The y intercept is when x = 0 so here it is

y = -25(0)^2 + 30(0) -9

= -9

The constant  at the end of the function (-9) indicates the y-intercept.

The y intercept is at (0, -9).

Part C.

The end behaviour of f(x):

The negative coefficient (-25) of x^2 indicates that the graph increases from negative infinity from the left.

Since it is a parabola that opens downwards  ( because of the -25)  it decreases to negative infinity on the right.

exa:

)

3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.