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.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

c

step-by-step explanation: