Please help! Mental block!

Solve the following inequation, expressing your answer in set notation:

x^2 - x - 5 < 0

and...

What is the equation of the porabola that goes through the points:

(0,0)

(1,-2)

(4,4)

please help~ i'm desperate! :(

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- April 22nd 2007, 05:08 AMgeorgiaaa.Quadratics Inequality
Please help! Mental block!

Solve the following inequation, expressing your answer in set notation:

x^2 - x - 5 < 0

and...

What is the equation of the porabola that goes through the points:

(0,0)

(1,-2)

(4,4)

please help~ i'm desperate! :( - April 22nd 2007, 05:56 AMThePerfectHacker
- April 22nd 2007, 06:23 AMSoroban
Hello, georgiaaa!

Quote:

Solve the following inequation, expressing your answer in set notation:

. . x² - x - 5 .< .0

We have an up-opening parabola. .When it is negative?

. . When it is*below*the x-axis.

When does that happen?

. . Let's find the x-intercepts.

. . . . . . . . . . . . . . . . . . . . . . __

. . . . . . . . . . . . . . . . . . 1 ± √21

Quadratic Formula: .x .= . ---------

. . . . . . . . . . . . . . . . . . . . .2

The expression is negative*between*those two intercepts.

. . . . . . __ . . . . . . . . . . . . . __

. . (1 - √21)/2 .< .x .< .(1 + √21)/2

Quote:

What is the equation of the parabola that goes through the points:

. . (0,0), (1,-2), (4,4)

Plug in the three points:

. . .(0,0): .a·0² + b·0 + c .= .0 . . → .**c = 0**

. . (1,-2): .a·1² + b·1 + 0 .= .-2 . → . . .a + .b .= .-2 .[1]

. . .(4,4): .a·4² + b·4 + 0 .= .4 . . → . 16a + 4b .= .4 . [2]

Divide [2] by 4: . 4a + b .= .1

. . Subtract [1]: . .a + b .= .-2

. . and we get: .3a = 3 . → .**a = 1**

Substitute into [1]: .1 + b .= .-2 . → .**b = -3**

Therefore, the parabola is: .**y****.= .x² - 3x**