1. How to Graph Quadratics in 3 Forms
Ecenur Karakoyun

2. Standard Form y=ax2 +bx+c
When graphing a standard form quadratic function, the value in front of x2 (a) shows if the graph is going upwards or downwards.
Also the value of a shows the wideness of the graph. If a>1, the graph is skinner than a<1.
Standard form also gives the y intercept ,which is c in the equation.
To find the x intercepts, factoring can make things very easy if the equation can be factored. If not, x intercepts can be found by using table of values and finding matching points.
The axis of symmetry can be found in the middle of x intercepts. Which can be calculated after factoring the equation if possible by adding the two intercepts and dividing them by 2.
The axis of symmetry is also the first value in the vertex. So, after writing it down it as x, the second value in the vertex is found.
Standard Form y=ax2 +bx+c

3. When graphing this equation, it is clear that graph is going upwards since the number in front of x2 (a) is positive (there is a secret+1).
The y intercept is (0,12) because c =12 in this equation.
This equation can be factored into (x+4) (x+3) which gives the x intercepts.
To find the x intercepts, the value inside the brackets should be equal to zero. In this point x+4=0 means x=-4, and x+3=0 means x=-3.
The axis of symmetry can be found after this step which is-3.5 (-3- 4/2). It is the first value in the vertex.
After writing -3.5 as x in the equation, the second value in the vertex is found, which is -0.25
Vertex for this equation is (-3.5,0.25) with the x intercepts of (-4,0) and (-3,0) and the y intercept of (0,12)
y=x2 +7x+12

4. The graph for the equation y=x2+7x+12

5. Factored Form y=a(x-s) (x-s)
When graphing a factored form of quadratic function, again a shows if the graph is upwards or downwards, within the width of the graph.
The x intercepts are the values which will make the values equal to zero in the brackets. For example (x-7) (x+4), in this case x intercepts would be (7,0) and (-4,0)
Axis of symmetry (first value in vertex) can be found easily just by adding the two intercepts together and dividing them by 2.
After putting the value of the axis of symmetry as x in the equation, the result would give the second value in the vertex.
To find the y intercept in factored form, x should be equal to zero. This means the y intercept is the value that is left when x is written as 0.
Factored Form y=a(x-s) (x-s)

6. X intercepts for this equation are (2,0) and (-3,0) because the value which will make x-2=o is 2, and the value which will make x+3=0 is -3.
The axis of symmetry (adding of x intercepts and dividing them by 2) is (-3+2/2=-0.5). This is the first value in the vertex.
The second value in the vertex is 12.5(the final value after putting as x)
Y intercept is (0,12), because x=0 while finding the y intercept. So for this equation when x is zero should be =12
The graph would go downwards since a is less than 0 (-2<0)
The vertex of this equation is (-0.5,12.5) with the x intercepts of (2,0) and (-3,0), and with the y intercept (0,12)
y= -2(x-2) (x+3)

7. The graph for the equation y=-2(x-2) (x+3)

8. Vertex Form y=a(x-p) 2+q
When graphing a vertex form quadratic function, p stands for x (the first value in vertex), and q stands for y (the second value in vertex).
The number in front, a, still shows if the graph goes upwards or downwards and shows the width.
Vertex form gives the vertex very easily, the opposite sign of the value, which is in the place of p, gives the first value in the vertex, and the exact value, in the place of q, gives the second value of the vertex.
The axis of symmetry is automatically given considering the fact that, the first value in the vertex is equal to the axis of symmetry.
To find the y intercept, the same rule is still valid, x should be equal to zero. Writing 0 as x and calculating would give the y intercept.
Vertex Form y=a(x-p) 2+q

9. The first value in the vertex would be +4 in this equation, because the first value in the vertex is the opposite sign of the value in the place of p.
The second value in the vertex would be +1 since the value in the place of q is equal to the second value and does not have to change its sign.
Y intercept would be (0,49) because x should be 0 in the equation which means 3.16 (0-4) 2+1=49
The vertex of this equation is (4,1) with the y intercept of (0,49) and the axis of symmetry=4.
The graph is going upwards since the a is positive (3>0).
y=3(x-4) 2+1

10. The graph for the equation y=3(x-4) 2+1