# a quadratic function has zeros at 1 and -3 and passes through the point (2,10). Write the equation in vertex form Hint: write the equation in standard form before vertex form. Hint: write all general formulas which you need to use

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A quadratic function has zeros at 1 and -3 and passes through the point (2,10).

(1) First we can write the function in intercept form: `y=a(x-p)(x-q)` where `p,q` are the x-intercepts (zeros, roots, etc...)

Thus we have `y=a(x-1)(x+3)` (Note that if k is a zero of a function, then (x-k) is a factor)

We need to solve for the coefficient a; we use the point (2,10):

`10=a(2-1)(2+3)`

`10=5a`

`a=2`

Thus we have `y=2(x-1)(x+3)`

(2) From here we can write in general form: `y=ax^2+bx+c` by...

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