Question

How?? I only know how to convert standard form functions into intercept form, but I do not understand how to do this.

Convert the functions into standard form.

1.y=2(x-4)(x+3)


2.y-2=-3(x+4)^2

Answer 1

Both of your equations are quadratics
the standard form, sometimes called the vertex form, of a quadratic takes the form
y = a(x-h)^2 + k , where the vertex is (h,k)

your first equation is in intercept form, so the x of the vertex must be midway between -3 and 4 which would be 1/2
sub in 1/2 for x to get y
y = 2(1/2-4)(1/2+3) = -49/2

so y = 2(x - 1/2)^2 - 49/2

another way would be to first expand it
y = 2(x^2 - x - 12) = 2x^2 - 2x - 24
now completing the square ....
y = 2(x^2 - x + 1/4 -1/4) - 24
= 2( x - 1/2_)^2 - 1/2 - 24
= 2(x-1/2)^2 - 49/2 , same as above

for your second, we are almost there, just add 2 to both sides

y = -3(x+4)^2 + 2

Answer 2

Oh okay thank you, it's very clear now!