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- Do you know what the vertex and axis of symmetry are? Today I am going to show you how to find both of these and plot them on the graph using an equation that is in vertex form!
- The equation below is written in vertex form. So whenever your equation looks like this, you will know how to graph it! The vertex of a parabola is the maximum or minimum point on the graph, depending on which way your line is facing. So (h, k) is the vertex of your equation. You will plot the point the same as if it was (x, y). For example, if this was your equation: f(x) = 3(x - 9)^2 + 5, then the vertex would be (9, 5). We can figure out that (9, 5) is our minimum value because the leading coefficient (3) is positive. This is what our equation looks like when graphed.
- f(x) = a(x - h)^2 + k
- Next I will show you how to find the axis of symmetry. It is very simple, and you're already halfway there! The axis of symmetry is a vertical line that passes through the vertex of a parabola. So the axis of symmetry is the x-value of the parabola. To find the axis of symmetry, we will use the vertex point, so (9, 5), if we use our previous example. The axis of symmetry is the x-value of the vertex, so it is 9.
- Do you notice how the axis of symmetry goes right through the vertex? That is just what you learned! Now that you know how to find and plot the vertex and axis of symmetry, let's test your skills! If you get stuck, I will be ready to help. You can always look back at what you learned here, too. You got this!
- Okay, so here is your equation. Remember, you want to find the vertex first because it is easier to find the axis of symmetry using the vertex. So figure out what the vertex is, and then we will see if you are correct. Do you think that the vertex is (4, 6)? If so, you are correct! If not, that is okay, I will walk you through it. We know that the vertex is (h, k), so looking at the numbers substituted into the equation, which ones are h and k. 4 is substituted for h, and 6 is substituted for k. So our vertex is (4, 6). Now what is the axis of symmetry? Here is a hint, it has something to do with the vertex. 4 is correct!
- Want to know why the line is upside down? That's because the leading coefficient (-11) is negative. This also means that the vertex is the maximum value.
- Here's why, remember that the axis of symmetry is a line that goes through the vertex. The axis of symmetry is only an x-value, the x-value of the vertex. So if the vertex is (4, 6), then the axis of symmetry is 4! Great Job! Now you are a graphing master! Want to see the graph of this equation? Here it is!
- f(x) = a(x - h)^2 + kf(x) = -11(x - 4)^2 + 6
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