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Math  /  Algebra

QuestionThe graph of a quadratic function with vertex (1,−4)(1,-4) is shown in the figure below. Find the domain and the range.
Write your answers as inequalities, using xx or yy as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) domain: □\square (b) range: □\square

Studdy Solution

STEP 1

1. The function is a quadratic function, which is a parabola.
2. The vertex of the parabola is given at the point (1,−4)(1, -4).
3. The parabola opens downward.

STEP 2

1. Determine the domain of the quadratic function.
2. Determine the range of the quadratic function.

STEP 3

The domain of a quadratic function is all real numbers because a parabola extends infinitely in both the left and right directions on the x-axis.
Domain: All real numbers

STEP 4

Since the parabola opens downward and the vertex is at (1,−4)(1, -4), the maximum value of the function is at y=−4 y = -4 .
The range of the function is all real numbers less than or equal to −4-4.
Range: y≤−4 y \leq -4
(a) domain: All real numbers
(b) range: y≤−4 y \leq -4

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