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2 years ago

Answer my questions plz help

Mathematics

1 answer:

coldgirl [10]2 years ago

3 0

9514 1404 393

Answer:

a = -2/3, b = 8, c = -24
y-intercept: (0, -24)
x = -b/(2a) = -8/(2(-2/3)) = 8(4/3)
x = 6
DOWN
Max: (6, 0)
Vertex: (6, 0)
Domain: {x | x ∈ ℝ}
Range: {x | x ≤ 0}

Step-by-step explanation:

To find a, b, c, compare the given function to ...

f(x) = ax² +bx +c

You will see that ...

a = -2/3
b = 8
c = -24

The y-intercept is the function value for x=0. It is the constant term:

y-intercept = f(0) = -24

Use the above values of a, b to find the line of symmetry.

$x = \dfrac{-b}{2a}=\dfrac{-8}{2\cdot\dfrac{-2}{3}}=8\cdot\dfrac{3}{4}=6$

Per the calculation, the line of symmetry is ...

x = 6

The negative leading coefficient tells you the parabola opens DOWN.

Because it opens down, the vertex at (6, 0) is a Maximum.

As with any polynomial, the domain is "all real numbers", hence any x that is an element of Reals.

The range is all values below the vertex (including the vertex), so is ...

x ≤ 0

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