A rectangular swimming pool is represented by x as the width and one less than twice the width as the length. If the area of the
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The value of a is 9, the correct option is B.
Given
Hank’s teacher asked him to verify that the product (y−3)(y2+3y+9), is a difference of cubes.
<h3>Quadratic equation;</h3>The equation which has the highest degree is 2 is called quadratic equation;
Where a, b, and c are the constants.
The given polynomial is;
On multiplying the terms;
On comparing;
Hence, the value of a is 9.
To know more about polynomial click the link is given below.
Answer:
see attached
Step-by-step explanation:
You can find the x-intercepts by factoring the equation:
y = -(x² -4x -5) = -(x -5)(x +1)
The x-intercepts (roots) are the values of x that make the factors zero:
x -5 = 0 ⇒ x = 5
x +1 = 0 ⇒ x = -1
The axis of symmetry is halfway between, at x=(5-1)/2 = 2.
For purposes of graphing, it is useful to use values of x that are on the axis of symmetry, and 1 unit either side.
For x=2, y = -(2 -5)(2 +1) = 9
For x=1, y = -1² +4·1 +5 = 8
For x=0, y = 0 +0 +5 = 5
The graph is symmetrical about the axis of symmetry, so you now have the points ...
(-1, 0), (0, 5), (1, 8), (2, 9), (3, 8), (4, 5), and (5, 0)
The vertex is (2, 9).
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<em>Additional comment</em>
The values 1 unit either side of the vertex differ from the vertex value by the amount of the leading coefficient. Here, that is -1, so the y-values for x=2±1 are 9 +(-1) = 8. This is useful to remember when you are writing equations from a graph.
