How to find turning point?

Question

hi, just a quick help, i need to know how to find the turning point for a quadratic equation with two brackets
for example:

(x+3) (x-8)
thanks

Answer 1

You need to complete the equation. I assume you mean:

y = (x + 3)(x - 8)

This is the equation of a parabola.

There are two ways of finding the vertex or turning point, one that involves calculus and one that does not. I assume that you have not yet taken calculus.

First, multiply out the equation.

y = (x + 3)(x - 8)
y = x² - 5x - 24

Now complete the square.

y = (x² - 5x + 25/4) - 24 - 25/4
y = (x - 5/2)² - 121/4
y + 121/4 = (x - 5/2)²

The turning point or vertex of the parabola is (5/2, -121/4).

Answer 2

The easiest way is to find the roots of the quadratic equation. Those are where (x+3)(x-8) = 0.
Obviously, for the equation to be zero, either (x+3) or (x-8) must be zero - otherwise you're multiplying two non-zero things together.
Hence, the roots are at x=-3 and x=8.

Since the graph of a quadratic equation is always a parabola, and parabolas are symmetrical, it follows that the vertex (or "turning point") is midway between -3 and 8.
The average of -3 and 8 is 5/2, so that's the x-coordinate of your vertex.

Answer 3

multiply it out then you differentitate and then put it equal to 0. this will give you max or min ie turning points.

so y=(x+3) (x-8)
y=x^2-5x-24

dy/dx = 2x-5
0=2x-5
x=5/2 is turning point

[differentiating a function gives the gradient and at a turning point the gradient is 0 so thats why you put dy/dx as 0]

Answer 4

f(x) = x² - 5x - 24
f `(x) = 2x - 5 = 0 for turning point
x = 5/2
f(5/2) = 25/4 - 25/2 - 24
f(5/2) = 25/4 - 50/4 - 96/4
f(5/2) = - 121/4
Turning point is (5/2, - 121/4)

Answer 5

if we consider quad. eqn in the form of
(x+n)(x+m)=f(x)
x^2-Sx+P=0
S is the summation of roots & P is the multiplication of roots;
so -(n+m)=S & P=m*n
the turning point is x=S/2 that is
x= -(n+m)/2
in this problem -(3-8)/2 which is 5/2=2.5
f of turning point comes from this simple formula
f(x)= -(S^2-4P)/4= -30.25