Which is the graph of f(x) = x2 – 2x + 3?

Asked by wiki @ 29/10/2020 in Mathematics viewed by 305 People

Answered by wiki @ 29/10/2020

The correct answer is:

The graph will be the same width as the parent graph f(x) = x², but the vertex has been shifted to (1, 2).

Explanation:

Since the value of a, the coefficient of x², is 1, this means the graph has not been stretched or shrunk. However, since the function is different than f(x)=x², we know that the vertex is not at (0, 0). We can write the function in vertex form to find the new vertex.

To write the function in vertex form, we find the value of b/2. The value of b in this function is -2; -2/2 = -1. We then square this: (-1)² = 1. This is what we add and subtract to the function (we must do both to preserve equality), giving us:

f(x) = x²-2x+1+3-1

The first three terms of this function can be written as the square (x+(b/2))²; this is (x-1)², and gives us f(x) = (x-1)²+3-1. Combining like terms, we have:

f(x) = (x-1)²+2

This is vertex form, f(x) = a(x-h)²+k, where (h, k) is the vertex. This means the vertex is at (1, 2) instead of (0, 0).

Which is the graph of f(x) = x2 – 2x + 3?

Similar Questions

Which is the graph of the function f(x) = x2 + 2x + 3?

Over which interval is the graph of f(x) = x2 + 5x + 6 increasing?

Over which interval is the graph of f(x) = –x2 + 3x + 8 increasing?

If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?

Which is the graph of the function f(x) = x2 + 2x – 6?

Which graph represents the function f(x) = |x + 3|?

Which graph models the function f(x) = −2(3)x?

Which graph represents the function f(x) = (x – 5)2 + 3?

The graph of f(x) = x2 is translated to form g(x) = (x – 2)2 – 3.

Which is the graph of f(x) = –(x + 3)(x + 1)?

Over what interval is the graph of f(x) = –(x + 8)2 – 1 decreasing?

Which graph has the same end behavior as the graph of f(x) = –3x3 – x2 + 1?

If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?

Which statement describes the graph of f(x) = –4x3 – 28x2 – 32x + 64?

Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?

Most viewed questions in Mathematics

Unit 6 similar triangles homework 2 similar figures answer key

All things algebra unit 7 polygons and quadrilaterals answer key

Gina wilson all things algebra 2016 answer key unit 11

Unit 1 geometry basics homework 4 angle addition postulate answers

Unit 6 exponents and exponential functions homework 8 answer key

The manager of a vacation resort believes that the ages

What is 271 403 rounded to the nearest ten thousand

Unit 1 geometry basics homework 3 angle relationships answer key

Homework 2 parallelograms

Why would a prism beat a sphere in a competition?

John wants to send a letter to peter

An artist sells a painting for 20.50 but uses 5.75

Unit 4 congruent triangles homework 1 classifying triangles answer key

Unit 4 congruent triangles homework 2 angles of triangles

Compare the values of the 2s and 5s in 55220