Math  /  Algebra

QuestionQuestion 4 (4 point) True or False: The graph of the following function would be narrower than the quadratic parent function: f(x)=2x2f(x)=2 x^{2} True False

Studdy Solution

STEP 1

What is this asking? Is the graph of f(x)=2x2f(x) = 2x^2 thinner than the graph of y=x2y = x^2? Watch out! Don't mix up "narrower" with "wider"!
A larger coefficient multiplying the x2x^2 term makes the parabola narrower, not wider.

STEP 2

1. Recall the role of the coefficient.
2. Compare the given function to the parent function.
3. Determine if the graph is narrower or wider.

STEP 3

Alright, let's break this down!
Remember, the **parent function** for a quadratic is y=x2y = x^2.
Any number multiplied in front of the x2x^2 term, like the **2** in f(x)=2x2f(x) = 2x^2, is called the **leading coefficient**.
This coefficient tells us how the parabola is stretched or compressed vertically.

STEP 4

Think of it like this: if the **leading coefficient** is *greater* than **1**, the parabola gets *narrower*, like someone's stretching it upwards.
If the **leading coefficient** is between **0** and **1**, it gets *wider*, like someone's squishing it down.

STEP 5

Our function is f(x)=2x2f(x) = 2x^2.
The **parent function** is y=x2y = x^2.
Notice that our function has a **leading coefficient** of **2**.

STEP 6

Since our **leading coefficient**, **2**, is *greater* than **1**, the graph of f(x)=2x2f(x) = 2x^2 is *narrower* than the graph of the **parent function** y=x2y = x^2.

STEP 7

True! The graph of f(x)=2x2f(x) = 2x^2 *is* narrower than the parent function.

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