Quadratic Functions

[johnmeyer]

Hi guys I have this homework problem maybe you could help me out

Determine an equation for the quadratic function with zeros of -2 + sqrt5 and -2 - sqrt5, containing the point (-4,5). Write the equation in factored, and standard form.

 

[jonah2.0]

Beer soaked ramblings follow.

Hi guys I have this homework problem maybe you could help me out

Determine an equation for the quadratic function with zeros of -2 + sqrt5 and -2 - sqrt5, containing the point (-4,5). Write the equation in factored, and standard form.

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[Harry_the_cat]

Hi guys I have this homework problem maybe you could help me out

Determine an equation for the quadratic function with zeros of -2 + sqrt5 and -2 - sqrt5, containing the point (-4,5). Write the equation in factored, and standard form.

If the zeroes of a quadratic function are p and q, then the factors are (x-p) and (x-q).
You are given p and q, so you should be able to form the function as y = a(x-p)(x-q).
Then sub in the point (-4,5) to find a.

Give it a go and see what you can do. Come back if you need further help.

 

[HallsofIvy]

You can write a quadratic function as $\displaystyle f(x)= a(x- x_0)(x- x_1)$ where a is some number and $\displaystyle x_0$ and $\displaystyle x_1$ are values of x such that f(x)= 0.

So we can write $\displaystyle f(x)= a(x- (-2- \sqrt{5}))(x- (-2+ \sqrt{5}))$. The multiplication is simplified if we use the fact that $\displaystyle (p- q)(p+ q)= p^2- q^2$ with $\displaystyle p= x+ 2$ and \(\displaystyle q= \sqrt{5}\(\displaystyle .

So $\displaystyle f(x)= a(x- (-2- \sqrt{5}))(x- (-2+ \sqrt{5}))= a((x+ 2)^2- (\sqrt{5})^2)= a(x^2+ 4x+ 4- 5)= a(x^2+ 4x- 1)$. All that is left is to determine a. To do that, use the fact that $\displaystyle f(-4)= a((-4)^2+ 4(-4)- 1)= a(16- 16- 1)= -a= 5.$\)\)