# Math (Help This Will Be on My Test Tomorrow!)

posted by .

y= ax^2+bx-4. How would i find the equation of this parabola with the points (0,-4) (1,0) (2,2) (4,0) and 6,-10)?

• Math (Help This Will Be on My Test Tomorrow!) -

Use the first few given points
for (0,-4) : -4 = 0 + 0 - 4 , nothing new learned here
for (1,0) : 0 = a + b - 4 ----> a+b+4 or b = 4-a
for (2,2) : 2 = 4a + 2b - 4 --- 2a + b = 3

use substitution
2a + (4-a) = 3
a = -1
then b = 4-(=1) = 5

y = -x^2 + 5x - 4
test if the other points satisfy, they do!

• Math (Help This Will Be on My Test Tomorrow!) -

You must write equation for any pair of points.

y=ax^2+bx-4

x=0 y= -4

-4=a*0^2+b*0+c

0+0+c= -4

c= -4

x=1 y=0

0=a*1^2+b*1-4

a*1+b*1-4=0

a+b-4=0

a=4-b

x=2 y=2

y=ax^2+bx-4

2=(4-b)*2^2+b*2-4

(4-b)*4+2b-4=2

16-4b+2b=2+4

-2b=6-16

-2b= -1 Divide with -2

b=5

a=4-b

a=4-5

a= -1

So:

a= -1 b=5 c= -4

y=ax^2+bx+c= -x^2+5x-4

y=-x^2+5x-4

Checking of results:

For x=4

y=ax^2+bx-4

y= -4^2+5*4-4

y= -16+20-4

y=4-4

y=0

Correct value

For x=6

y=ax^2+bx-4

y= -6^2+6*5-4

y= -36+30-4

y= -6-4

y= -10

Correct value

• Math (Help This Will Be on My Test Tomorrow!) -

I make one mistake in typig.

-2b= -1 Divide with -2 is mistake

-2b= -10 Divide with -2 is correct

## Similar Questions

1. ### Quadratic Equations and Functions

I started having trouble on part (c), and I need to know this before I can go onto the other problems. Plz help! The parabola shown at the right (no picture, sorry) is of the form y=x^2+bx+c. The graph's y-intercept is (0,2), the axis …
2. ### Quadratic Equations and Functions

I started having trouble on part (c), and I need to know this before I can go onto the other problems. Plz help! The parabola shown at the right (no picture, sorry) is of the form y=x^2+bx+c. The graph's y-intercept is (0,2), the axis …
3. ### math

HISTORY TEST You take a history test that has 100 regular points and 8 bonus points. You get a score of 91, which includes 4 bonus points. Let x represent the score you would have without the bonus points. Which equation represents …
4. ### Math

I need help in finding the vertex of a parabola using an equation in this form: Ax^2 + Bx+C I have a test on this tomorrow. For example: 3x^2 +1x - 2 How would I find the vertex in this?
5. ### math-geometry

we have a test tomorrow and she said that a problem like this is going to be on there how do you do it?
6. ### MATHS

a parabola passes through the points (1,1) , (2,0) and (3,1) the equation of the parabola is y=ax^2 + bx + c a) write down a system of equations representing this parabola. b) solve the corresponding system and hence write down the …
7. ### pre cal

What is the center of the conic whose equation is x^2 + 2y^2 - 6x + 8y = 0 2.Which one of the following equations represents a hyperbola?
8. ### MATH

a parabola passes via the points (1.5,1) and (3,-5). given that the vertex lies on the line 7x+3y-4=0,find the focus and the equation of the parabola
9. ### Math - Quadratics & Analytical Geometry

I have a test tomorrow with a few sample questions that are expected to be on the test that I do not know how to properly do. 1)Find the slope intercept equation of the line passing through the intersection of the lines 2x-4y=1 & 3x+4y=4 …

I have a test tomorrow with a few sample questions that are expected to be on the test that I do not know how to properly do. 1)Find the slope intercept equation of the line passing through the intersection of the lines 2x-4y=1 & 3x+4y=4 …

More Similar Questions