answer question 15 using the graph below ### Problem 15Given the parabola $ y = f(x) $ as shown in the graph:#### Tasks:**a.** Find $ f(3) $ and $ f'(3) $.**b.** Hence find $ f(x) $ in the form $ f(x) = ax^2 + bx + c $.#### Explanation of the Graph:The graph displays a parabola $ y = f(x) $ with a vertex at the minimum point and a symmetrical shape about the vertical axis. The x-axis and y-axis are labeled. There is a point on the parabola at $ x = 3 $, where the parabola intersects a horizontal line at $ y = 5 $. The tangent to the curve at this point is shown in green crossing the x-axis to the right of the y-axis. The y-axis is marked at intervals, extending up to 14. The goal is to determine the specific value of the function and its derivative at $ x = 3 $ and use this to derive the quadratic function's equation.

Answered: Image /qna-images/answer/bac97f00-6ebd-4ce4-95b2-ce64e3de7a99.jpg

Answered: 15 y = f(x) is the parabola shown. a…

Math

Calculus

15 y = f(x) is the parabola shown. a Find f(3) and f'(3). b Hence find f(x) in the form f(x) = ax² + bx + c. 14 y=f(x)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: For the graph below, choose most appropriate option at the point z = 0.

A: Question is solved.

Q: 2. An oven technician charges a call-out fee of $50 and an additional $20 per hour for the duration…

A: The call out fee is $50 additional fee per hour = $20 per hour let t be the number of hours…

Q: Describe the graph of the equation 4x² - 9y + 16x + 54 y - 29 =0.

A: Consider the given equation 4x2-9y2+16x+54y-29=0…

Q: Compared to the graph of y = 7 X, the graph of y = 0.7* is A. "skinnier" and pulled closer to the…

A: To compare: The graph of . Explanation: The graph of represents that the graph is increasing graph…

Q: 4- 34 2. Given the equation y =x - 3 2- b(y-intercept) = m= 4. 3 24 3 4- 2.

Q: Which of the following is the graph of y = -2cos

A: The given equation is y=-2cosπ3x.

Q: 24 35 46 57 68 79 06 101 112

A: Given that Graph of exam scores. The graph is bell shaped so, it is normally distributed. The…

Q: Identify the correct equation for the graph below. * y. O y =2x + 3 O y = 1/2x + 3 O y = 1/2x - 3 O…

Q: The number N (in millions) of cellular phone subscribers is shown in the table. (End of year…

Q: Question 27 A scientist modeled the height of an object (h(t) measured in kilometers, t measured in…

Q: Write an equation for the graph below in terms of a 4- -3 -2 - 2 3 -2 -3 -4 > Next Question to

Q: Isabel starts a new job, this time painting a metal fence at a steady rate. She paints all morning…

Q: Write an equation for the graph below in terms of x 2 -3 -2 -4 -51 y = on 3. 3.

Q: 5. Two brothers, Leo and William, are racing their bikes around a 9,5-kilometer loop. Since Leo is…

Q: Does the graph of Y1 pass through the origin?

A: Consider the following table:

Q: -6 -5 -4 -3 -2 A CON 7 654 on 44 -4 -2 -3- --4-- -5 --6- flot 3 4 5 Find an equation for the graph…

A: We can see that the graph is modified form of f(x) = sec x which is vertically stretched thrice. So,…

Q: Which of the following is true? А. lim Ax) =- and lim fx)=-0 x→ 3- x → 3* В. lim f(x) = -00 and lim…

Q: < co %24 3. Question 9 Graph: y- < -1 1. 2. 4. 2. -5 -4 -3 -2 -1 2 3 4 -2 -5 Clear All Draw:…

Q: QUESTION 23 The graph below would most likely be represented by a linear function with ty O A.…

A: The objective is to find the correct option.

Q: -6 -5 -4 -3 -3 -2 8 HAP 7 6. 5 4 327 -1 -2 -7 1 2 ton 3 4 5 Find an equation for the graph above.…

A: Given is a graph To Find: an equation for the given graph

Q: 17. The graph below represents y = -2x. Which describes how this graph would need to be shifted in…

Q: Below is the graph of y=x". Transform it to make it the graph of y=-3(x-2).

Q: Select the equation that matches the graph shown below. O y= r +2x - 3 O y = -I- 3 Oy = r-2r- 3 Oy =…

A: From the design of the graph , we can say that it is a parabola. The vertex of the graph is at (1,…

Q: Graph: +. <1 4. 5+ /3

Q: Give three observations that can be made from the graph. Monthly Active Users on 5 Social Networking…

A: Most users means maximum frequency of the observations and the lowest frequency means the lowest…

Question

answer question 15 using the graph below

### Problem 15

Given the parabola $ y = f(x) $ as shown in the graph:

#### Tasks:

**a.** Find $ f(3) $ and $ f'(3) $.

**b.** Hence find $ f(x) $ in the form $ f(x) = ax^2 + bx + c $.

#### Explanation of the Graph:

The graph displays a parabola $ y = f(x) $ with a vertex at the minimum point and a symmetrical shape about the vertical axis. The x-axis and y-axis are labeled. There is a point on the parabola at $ x = 3 $, where the parabola intersects a horizontal line at $ y = 5 $. The tangent to the curve at this point is shown in green crossing the x-axis to the right of the y-axis. The y-axis is marked at intervals, extending up to 14.

The goal is to determine the specific value of the function and its derivative at $ x = 3 $ and use this to derive the quadratic function's equation.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find Limit (x -> 5) (4x2 -12x-40)/(2x-10)
What is the answer?
Consider the following graph. Step 2 of 2: Determine the x-coordinates of any inflection point(s) in the graph. Answer How to enter your answer (opens in new window) Separate multiple entries with a comma. -10 -5 Inflection point(s) at x = 15 7.5 -7.5 -15 Enable Zoom/Pan 3 10 X Previous step Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used. K Keyboard S None
H Cale Find an equation for the graph sketched below: -5-4-3-2 f(x) = 84 7 36 5 3 2 my 72 -2 -7 -8 2 3 4 5 d
The graph from question five is reproduced below. Click on the location (coordinates) where the drug concentration is at a maximum. 10- -4 -2 4 -10- Selected Coordinates Clear
Identify the correct equation for the graph below. * -4 -2 0 -2 O y =2x + 3 O y = 1/2x + 3 O y = 1/2x - 3 O y = -1/2x - 3 4. 2.
Answer given question.
Answer given question.
E A to 1 B Consider the point x₁ C undefined 1 D X₂ f(x) x3 = 0.75 * x₁ +0.25 * x₂ X Which of the points on the x-axis, C or D, represents this point?