How to make graph

Y = x² +2x-24

After we got the problem as stated above, the first determine whether the equation open upward or downward open. Open up if the equation is negative and opens down if the equation is positive. See how variable is the power, if the variable positive, then open down and open up when negative. If we look at the equation above, then the equation is open downward. Then we follow the step like this.

1. Determine intersect point of X_1,2  axis, y = 0 Use factorization / ABC Formula HP = {(x_1, 0), (x₂, 0)}

            Y = x² +2x-24

(x, 6) and (x,-4)

So, x₁ = -6 and x₂ = 4.

2. Then determine intersect point of y, x = 0 y = c -> HP = (0, c)

Y = x² +2x-24

Y= (0)² + 2(0) – 24

Y= -24.

3. Now we can sign the point of (x_1, 0), (x₂, 0) and (0, c) from twice the step above.

 Now we specify the symmetry line or a line for both sides halfway between -6 and 4 is -1. So we get the 4^th step and then we can prove the formula

4. The line of symmetry x = -

Then we have last step with

5. Determine the extreme/ vertex point HP = (-  or HP = ( x, f(x))

We can change the x point with some number to know the whole of the combined form of graphs and sketches.

Example: x {-5,-4,-3,-2,-1, 0, 1, 2, 3, 4, 5}

Y = (-5)²+2(-5)-24

   = 25-10-24

   = -11

Y = (-4)²+2(-4)-24

   = 16-8-24

   = -16

Y = (-3)²+2(-3)-24

   = 9-6-24

   = -21

Y = (-2)²+2(-2)-24

   = 4-4-24

   = -24

Y = (-1)²+2(-1)-24

   = 1-2-24

   = -25

Y = (-0)²+2(0)-24

   = 0-0-24

   = -24

Y = (1)²+2(1)-24

   = 1+2-24

   = -21

Y = (2)²+2(2)-24

   = 4+4-24

   = -16

Y = (3)²+2(3)-24

   = 9+6-24

   = -9

Y = (4)²+2(4)-24

   = 16+8-24

   = 0

Y = (5)²+2(5)-24

   = 25+10-24

   = -11

So graph is like below.