Answer: 0.75
Explanation: a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number
It’s 10 points not 20
Explanation
Answer:
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.
