# 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

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

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

## 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