Question

write a quadratic function that fits the points (0,5), (3,8), & (4,13).

<< correct answer : f(x)=x^2-2x+5 >>

Answer 1

The general form of q quadratic equation is:
y = ax^2 + bx + c
You have three unknowns here: a, b and c.
You are given 3 points.
Put the x,y values of each point in the equation and you will have 3 equations.
Three unknowns, three equations. You can solve for a, b and c.

Answer 2

First point is (0, 5). Put x = 0, y = 5 in
y= ax^2 + bx + c
5 = 0 + 0 + c
So c = 5
So our quadratic equation now is: ax^2 + bx + 5

Second point is (3,8). Put x = 3, y = 8 in
y = ax^2 + bx + 5
8 = a(9) + 3b + 5
9a + 3b = 3 -------- equation (1)

Third point is (4, 13). Put x = 4, y = 13 in
y = ax^2 + bx + 5
13 = a(16) + 4b + 5
16a + 4b = 8 -------- equation (2)

Eliminate b from equations 1 and 2
Multiplying equation 1 by 4:
36a + 12b = 12 -------- equation (3)
Multiplying equation 2 by 3:
48a + 12b = 24 -------- equation (4)
Subtract equation 3 from 4:
12a = 12
So a = 1
Put a=1 in equation 3:
36 + 12b = 12
12b = -24
b = -2

So we have a = 1, b = -2 and c = 5 for the equation
y = ax^2 + bx + c
y = (1)x^2 + (-2)x + (5)
y = x^2 - 2x + 5

Answer 3

oh my god thank you so much

Answer 4

you are welcome.

Answer 5

Is this Algebra 2 or linear algebra?

Answer 6

Alg II

Answer 7

okay good to know. @ranga did a good job.

Answer 8

Thanks @wio