Question

I need help creating a quadratic function with two real zeros. Will give medal to best answer (:

Answer 1

Oops + fan

Answer 2

Choose your two favourite real numbers. Think of them as 'a' and 'b'. Then your quadratic function is (x-a)(x-b).

Answer 3

I thought a function was F(x)

Answer 4

as BillBell said suggested.... do like so

Answer 5

I am confused though :/

Answer 6

ok.... have you covered quadratics yet?

Answer 7

Yeah the unit I am on is actually called Quadratic functions but my lessons aren't exactly well on explaining

Answer 8

ok... well. lemme .. pick a quick example \(\large {y=x^2+3x-4\implies 0=x^2+3x-4\implies 0=(x+4)(x-1)
\\ \quad \\
meaning\implies (x+4)(x-1)\implies
\begin{cases}
x+4=0\implies x=-4
\\ \quad \\
x-1=0\implies x=1
\end{cases} }\)

so if for example, you pick 2 values for "x", any values really, as BillBell suggested, let's say "a" and "b", which could be anyting
then
\(\large \begin{cases}
x=a\implies x-a=0
\\ \quad \\
x=b\implies x-b=0
\end{cases}\implies
\begin{array}{llll}
(x-a)(x-b)=0
\\ \quad \\
(x-a)(x-b)=\textit{original function}
\end{array} \)

Answer 9

and "a" and "b" can be pretty much anything, then just do a FOIL and that'd give the origiinal function

Answer 10

So If i choose
(x-2)(x-4)
My answer would be x^2-4-2x-8? I am sorry if its wrong or if i got the signs wrong

Answer 11

\(\bf (x-2)(x-4)\implies x^2-4x-2x+8\implies x^2-2x+8\) yes

Answer 12

Ohh i see I forgot to put the x after the 4 and how did you get the +8?

Answer 13

To answer your question about what a function is, there are a few ways of thinking about them. One simple way is that a function takes numbers and converts them into other numbers. For example, (x-2)(x-4) is a function in that it can take the number 2 and convert it to 0; it takes the number 3 and converts it to 1. In fact, this is a function that can convert any number (that you are likely to think of) into another number. If you wanted to give it a name for convenience you _could_ call it F(x) but this name wouldn't really tell you much about the function.

Answer 14

\[( x - 2 ) ( x - 4 )\]
expanding the first part
\[= x ( x - 4 ) - 2 ( x - 4 )\]
multiplying out the first parenthesised expression
\[= x ^{2} - 4x - 2 ( x - 4 )\]
now multiplying out the second one
\[= x ^{2} - 4x - 2x + 8\]
collect all the x-squared terms (just one), all the x terms (two), all the number terms (one)
\[= x ^{2} - 6x + 8\]

And, mercifully, we're finished.