Graphing Vertex Form
To graph a vertex form, you will need to know the step pattern. The step pattern we use goes by 1,4,9,16. These are the number of steps we make when plotting points to construct the parabola. When plotting the points we always move 1 to the left from the vertex and 1 up, then move 1 left again, and this time 4 up, continuing the pattern. You also do this to the right side as well. To graph the equation, multiply the step pattern by "a", (e.g. if a=2, (1,4,9,16)x2).
To evaluate the parabola, we must look at certain things. We must look at the vertex, the axis of symmetry, the optimal value, and whether the parabola is concave up or down. To find the x and y values from the equation is simple. "h" is the x value, and "k" is the y value. They are written as (h,k) like (x,y). The axis of symmetry is only the "h". In the equation it is referred to "-h" so whatever the value as "h", the sign is always switched, (e.g. if y=-2(x-2)^2=4 then the axis of symmetry is x=2). The optimal value is "k" and is written as y=4. To determine if the graph is concave up or down, we look at "a".If "a" is positive then the graph will go up (concave up) but if "a"is negative then the graph will go down.
If we were to solve an equation, y=x^2+3. We can see that there is no number in front of "x" so we know that there is always 1. So your step pattern doesn't change. There also isn't an "h" so we use that as zero. The y axis is the only one changing. Then the "k" is 3, so we move 3 up from the vertex, since it's positive. Then you plot the step pattern points to finish the parabola.
Difference of Squares-Factoring
Solving Equations by Factoring
Next we can find the axis of symmetry by implementing a formula, -b/2a."b" sign must change when putting it in the formula. -1/2(1) is what we are left with. When you solve this, we will get -0.5. This will be our axis of symmetry. And finally, plot the point and draw a vertical line to indicate the axis of symmetry, and use the step pattern to complete the graph.
b^2 - 4ac