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Math  /  Algebra

QuestionThe plot of what function appears below? f(x)=−(x+1)2f(x)=-(x+1)^{2} f(x)=−(x−1)2f(x)=-(x-1)^{2} f(x)=x2f(x)=x^{2} f(x)=(x−1)2f(x)=(x-1)^{2}

Studdy Solution

STEP 1

1. The graph is a parabola.
2. The vertex of the parabola is at the point (-1, 0).
3. The parabola opens downward.

STEP 2

1. Identify the general form of a parabola.
2. Determine the vertex form of the parabola.
3. Match the vertex and direction with given options.

STEP 3

The general form of a parabola is f(x)=a(x−h)2+k f(x) = a(x-h)^2 + k , where (h,k) (h, k) is the vertex.

STEP 4

The vertex of the parabola is given as (−1,0)(-1, 0), so the equation in vertex form is f(x)=a(x+1)2+0 f(x) = a(x+1)^2 + 0 .

STEP 5

Since the parabola opens downward, a a must be negative, so the equation becomes f(x)=−(x+1)2 f(x) = -(x+1)^2 .

STEP 6

Compare the derived equation f(x)=−(x+1)2 f(x) = -(x+1)^2 with the given options:
- f(x)=−(x+1)2 f(x) = -(x+1)^2 matches the derived equation. - f(x)=−(x−1)2 f(x) = -(x-1)^2 does not match; it has a vertex at (1, 0). - f(x)=x2 f(x) = x^2 opens upward and has a vertex at (0, 0). - f(x)=(x−1)2 f(x) = (x-1)^2 opens upward and has a vertex at (1, 0).
The function that matches the plot is:
f(x)=−(x+1)2 \boxed{f(x) = -(x+1)^2}

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