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AlexFokin [52]
2 years ago
6

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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