Section 9-5: Parabolas Recall that Parabola will result in a U shape curve. In chapter 5 we looked at Parabolas that opened up or down, now we will look at ones that also open left and right. If it has an x2 it will open If it has a y2 it will open up or down. left or right. 1

In chapter 5 the general equation for a parabola opening up or down was: Now the general equation for a parabola opening to the left and right is: Recall that in both cases we will need to find the x or y intercept depending on which way it opens and then a point of symmetry. 2

Example: Graph 3 Isolate the y values and factor if needed to get a coefficient of a 1 for y 2 Divide the y term by 2 and square, add the result to both sides. Simplify the left, write the right as a binomial square Now we can see that our vertex is (-7,2). We can tell that our x-intercept is (-3,0) and the point of symmetry is (-3,4)

Example: Graph 4 Isolate the y values and factor if needed to get a coefficient of a 1 for y 2 Divide the y term by 2 and square, add the result to both sides. Remember to multiply by the -2 first. Simplify the left, write the right as a binomial square Now we can see that our vertex is (8,3). We can tell that our x-intercept is (-10,0) and the point of symmetry is (-10,6)

Example: Graph 5 Isolate the y values and factor if needed to get a coefficient of a 1 for y 2 Divide the y term by 2 and square, add the result to both sides. Remember to multiply by the 1/2 first. Simplify the left, write the right as a binomial square Now we can see that our vertex is (-1/2,-3). We can tell that our x-intercept is (4,0) and the point of symmetry is (4,-6)

Example: Graph 6 Isolate the y values, in this case make sure to get the x positive by dividing by -1 Divide the y term by 2 and square, add the result to both sides. Remember to multiply by the 2 first. Simplify the left, write the right as a binomial square Now we can see that our vertex is (-7,3). We can tell that our x-intercept is (11,0) and the point of symmetry is (11,6)

Example: Graph 7 Isolate the x values and factor if needed to get a coefficient of a 1 for x 2 Divide the y term by 2 and square, add the result to both sides. Remember to multiply by the -4 first. Simplify the left, write the right as a binomial square Now we can see that our vertex is (2.5,9). We can tell that our y-intercept is (0,-16) and the point of symmetry is (5,-16)

Homework: Page Questions 2-14 evens 8