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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.
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
the idea being, you multiply the "x" by some power of 10 that moves the repeating part to the left of the decimal point and the split it like above.