Quadratic Function

[Guest]

The graph of a quadratic function meets the x-axis at the points (-4, 0) and (-2, 0). Given that the graph of the function also passes through the point (-8, 72), find the quadratic function in the form of y=ax^2+bx+c, where a, b and c are rational numbers.
Please help! Thanks!

[Guest]

You have to write a system of 3 equations with 3 variables - a, b and c.
Replace x and y with the given coordinates. Is it clear?

[Guest]

Can we not just keep it simple.......
and notice we are given the roots of the quadratic, from which we can find the factors that make up the general form of the solution.
And then we are given a point on the line that satisfies the equation......from which helps find the actual equation from the general form.

[Guest]

The roots are the points (-4, 0) and (-2, 0)

So (x + 4)(x + 2) = 0

So x^2 + 6x + 8 = 0 .....the general form of the equation

But this may have be multiplied or divided by a factor to simplify the solution ...

So... Let "a" be the factor

Then...... a(x^2 + 6x + = 0

OR at the 3rd point given a(-8^2 + 6times-8 + = 72

So..... 64a - 48a + 8a = 72

....... 24a = 72

a = 3


So quadratic is..... 3x^2 + 18x + 24 = y

a = 3, b = 18, c = 24

[Guest]

Can anyone tell me why I see smileys for the last term in the brackets when I posted the last post..
I am posting these lines again to see will it happen again. The last term in the brackets should be (plus eight).....

Then...... a(x^2 + 6x + = 0

OR at the 3rd point given a(-8^2 + 6times-8 + = 72

[Guest]

Yes it happened again....is it my browser OR does everyone else see smileys a swell...?????

[Guest]

[tex]8)[/tex] gets automatically converted to a smilie .
Either put a space between the 8 and bracket, or use tex tags
[tex]\text{[tex]8)[/tex]}[/tex]
to get
[tex]8)[/tex]

Hope this helped,

R. Baber.

[Guest]

Ok, thanks, I must try it....

3(2 x 4 + 5) = 3(5 +

[tex]3(2 x 4 + 5) = 3(5 + [/tex]

[Guest]

[tex]3(2 \times 4 + 5) = 3(5 + 8)[/tex]

[tex]3(2 \times 4 + 5) = 3(5 + 8)[/tex]

[Guest]

Code: Select all

[tex]3(5 + 8)[/tex]

[Guest]

I think it is easier to do maths than learn tex...........but I will read up on it...?????

[Guest]

You might want to lookup latex instead of tex (latex is more common than plain tex nowadays). If you want to try out latex you can go to
www.overleaf.com
It provides a free online latex environment (make sure you click the button to change from rich text to source).
Also check out
www.latex-tutorial.com/tutorials/beginners/lesson-4/
to get the basics.

This site doesn't provide all the features of latex but it provides the inline math environment (denoted by dollar signs in latex) by the use of the tex tags ([ tex] and [ /tex]).

(Also I think there is a slight bug in the website whereby sometime "8 )" sometimes becomes a smilie even in the tex environment.)

Hope this helped,

R. Baber.

[Guest]

You don't need to sign up to use overleaf.com you just need to click the "Create a new paper" button.

[Guest]

Thanks, ......the tutorial seem very good.......
[tex]\sqrt(1 +2) = 3x[/tex]

[Guest]

[tex]\sqrt(1+2) = 3x
3 = 9x^2
x^2 = \frac{1}{3}
x=\sqrt(\frac{1}{3}[/tex]

[Guest]

a few wee bits missing......newlines and brackets.....but I will get there....Thanks.