algebra

Given the following three points, find by hand the quadratic function they represent.

(0,6), (2,16), (3, 33)


- f(x)=−4x2−3x+6
- f(x)=4x2+3x+6
- f(x)=−4x2+21x+6
- f(x)=4x2−3x+6

I am struggling a lot with this one. But i think its A

  1. 👍 0
  2. 👎 0
  3. 👁 438
  1. Quadratic function:

    y = a x² + b x + c

    In this case:

    for x = 0 , y = 6

    y = a x² + b x + c

    6 = a ∙ 0² + b ∙ 0 + c

    6 = 0 + 0 + c

    6 = c

    c = 6

    Your quadratic function become:

    y = a x² + b x + 6

    for x = 2 , y = 16

    y = a x² + b x + 6

    16 = a ∙ 2² + b ∙ 2 + 6

    16 = 4 a + 2 b + 6

    Subtract 6 to both sides

    10 = 4 a + 2 b

    4 a + 2 b = 10

    Divide both sides by 2

    2 a + b = 5

    for x = 3 , y = 33

    y = a x² + b x + 6

    33 = a ∙ 3² + b ∙ 3 + 6

    33 = 9 a + 3 b + 6

    Subtract 6 to both sides

    27 = 9 a + 3 b

    9 a + 3 b = 27

    Divide both sides by 3

    3 a + b = 9

    Now you must solve system:

    2 a + b = 5 , 3 a + b = 9

    2 a + b = 5
    -
    3 a + b = 9
    _________
    - a = - 4

    Multiply both sides by - 1

    a = 4

    Replace this value in equation:

    2 ∙ 4 + b = 5

    8 + b = 5

    Subtract 8 to both sides

    b = - 3

    So:

    a = 4 , b = - 3 , c = 6

    y = a x² + b x + c

    y = 4 x² - 3 x + 6

    1. 👍 2
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. MATH

    Check It For Me Pleaseee Question 1 A) How do you know whether a relation is a function?(1 point) -By determining if each value from one set maps to another set such that each element of the domain pairs with exactly two elements

  2. Math help and check

    Which kind of function best models the set of data points (–1, 22), (0, 6), (1, –10), (2, –26), and (3, –42)? linear **** quadratic exponential none of the above 2. Which kind of function best models the set of data points

  3. Math

    Question 2 For the function f(x) = 3x2-2x-7, find f(2). Answer f(2) = 13 f(2) = 25 f(2) = 1 f(2) = 1/2 3 points Question 3 One day you work 3 hours and your boss gives you $22. Another day after working 4 hours your boss gives you

  4. Algebra

    Please Help! Given the following three points, find by hand the quadratic function they represent. (−1,−8), (0,−1),(1,2) A. f(x)=−3x2+4x−1 B. f(x)=−2x2+5x−1 C. f(x)=−3x2+10x−1 D. f(x)=−5x2+8x−1 Determine if

  1. math

    this question concerns the function f(x)=-2x3+3x2+12x+10 (a)find the stationary points of this function using the strategy to apply the first derivative test,classify the left hand stationary point found in part (a) find the

  2. Algebra

    Please help.! 1) Given the following three points, find by hand the quadratic function they represent. (0,6), (2,16), (3, 33) A. f(x)=4x2−3x+6 B. f(x)=4x2+3x+6 C. f(x)=−4x2−3x+6 D. f(x)=−4x2+21x+6 2) Given the following

  3. Pre-Calc

    A quadratic function has its vertex at the point (-5,-2). The function passes through the point (-8,-10). Find the quadratic and linear coefficients and the constant term of the function.

  4. Math

    ) A car dealership advertises a 15% discount on all its new cars. In addition, the manufacturer offers a $1000 rebate on the purchase of a new car. Let x represent the sticker price of the car. a. Suppose only the 15% discount

  1. math

    Part A: Does the table represent a relation that is a function? Justify your answer by using the values shown in the table. (4 points) Part B: The function f(h) shown below represents the number of tennis matches Diana won each

  2. College Algebra

    The graph of a quadratic function f(x) is shown above. It has a vertex at (-2,4) and passes the point (0,2). Find the quadratic function y=a(x-(-2))^2+4 y=a(x+2)+4 2=a(x+2)+4 -4 -4 -2=a(0+2)/2 -1+ a function -1(x+2)+4 ? Im not

  3. Mathematics

    Table of values represent a QUADRATIC FUNCTION OR NOT

  4. algebra

    The table shows a meteorologists predicted temperatiures for an April day in Washington D.C. Use quadratic regression to find a quadratic model for this data. Use the 24 hour clock to represent times after noon). time predicted

You can view more similar questions or ask a new question.