Studdy AI Logo
Math  /  Algebra

QuestionThe plot of what function appears below? f(x)=x2f(x)=x^{2} f(x)=−(x−1)2f(x)=-(x-1)^{2} f(x)=−x2+1f(x)=-x^{2}+1 f(x)=−(x+1)2f(x)=-(x+1)^{2} f(x)=(x−1)2f(x)=(x-1)^{2}

Studdy Solution

STEP 1

1. The graph is a parabola that opens downwards.
2. The vertex of the parabola is at the point (1,0) (1, 0) .

STEP 2

1. Identify the general form of a downward-opening parabola.
2. Determine the vertex form of the parabola.
3. Match the vertex form with the given options.

STEP 3

A downward-opening parabola is generally represented by the function f(x)=−a(x−h)2+k f(x) = -a(x-h)^2 + k , where (h,k) (h, k) is the vertex.

STEP 4

Given that the vertex of the parabola is (1,0) (1, 0) , substitute h=1 h = 1 and k=0 k = 0 into the vertex form: f(x)=−a(x−1)2+0 f(x) = -a(x-1)^2 + 0 f(x)=−a(x−1)2 f(x) = -a(x-1)^2

STEP 5

Compare the derived function f(x)=−a(x−1)2 f(x) = -a(x-1)^2 with the given options. The option that matches this form is: f(x)=−(x−1)2 f(x) = -(x-1)^2
The function that matches the plot is:
f(x)=−(x−1)2 \boxed{f(x) = -(x-1)^2}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord