### Vertex form presentation

Transcript: Now that we have the vertex, we can use a step pattern to find the next points on the parabola. Every step pattern is originally, (1,3,5,7 etc.) but you need to multiply each step by the value of a if there is one. To use a step pattern, you always move one unit horizontally and then vertically by the value of the step in each direction. Since the a value of this equation is -3, our step pattern is (-3,-9,-15,-21). Vertex form presentation quadratic equations To show how to graph a quadratic equation, I'll use the equation, y=-3(x+7)²-12 as an example. There are two types of quadratic equations; standard form and vertex form. Standard form is ax²+bx+c, but this form isn't easy to get data or graph it. This is why vertex form is useful; in the form a(x - h)²+k, you can easily determine the location of the vertex and find out if the parabola opens up or down or even if it is modified to be more stretched or compressed. To find the vertex, all you need to know is the x-value of the vertex is the same value as h, and the y-value is k. The variable a shows that the parabola was stretched if it's value is >0, or compressed if the value is <0. To see if the parabola opens up or down, simply look to the x²; if it's negative, the parabola opens down and if it's positive it opens up. Now that the parabola is formed, we need to double check to make sure it fits the equation. To do this we can take a point from the parabola, and plug it into the equation to see if it's still correct. I used (-5,-24) and plugged it in: -24=-3(-5+7)²-12 -24=-3(4)-12 -24=-12-12 -24=-24 Since the point fits the equation, we know that it is a point on the parabola. The first step is to find the vertex of the parabola; to do this, you need to identify the x and y values from the equation. Since we know the variable -h= the x-value of the vertex, and -h=7 we can determine that the x of the vertex is -7. The k is equal to the vertex's y-value, so we also know the y value is -12, meaning the vertex= (-7,-12). To graph a parabola Company Logo