VERTEX OF QUADRATIC FUNCTION HOW TO
We would need more information to find the y-coordinate of the vertex (without more information, we don’t even know if the parabola is concave or convex!) How To Find The Vertex Of A Parabola From A Graph
Taking the average of the two x-values, we get (3 + 9) / 2 = 6. This means that the parabola will intersect this horizontal line at two points that are the same distance from the line of symmetry (the horizontal line x = h, which goes through the vertex). Since the y-coordinates are the same (both are y = 7), we know that these two points lie on the same horizontal line (y = 7). Let’s say we have two points (3, 7) and (9, 7) that lie on a parabola. Example: How To Find The Vertex Of A Parabola From Two Points (Symmetry) We can use this to our advantage to take the average of these two x-coordinates to find the x-coordinate of the vertex. Since a parabola has symmetry, a horizontal line y = d will intersect the parabola at two points that are an equal distance from the vertex (or from the line of symmetry). This is due to the symmetry of a parabola about the line x = h (where h is the x-coordinate of the vertex).
If we have two points on a horizontal line that are equidistant from the vertex, then we can find the x-coordinate. How To Find The Vertex Of A Parabola From Two Points (Symmetry) The parabola y = 2x 2 -12x + 16 has its vertex at the point (3, -2). You can also see this in the graph below. So, the vertex of the parabola is (3, -2), just as we found before. We can also find this with our formulas that involve a, b, and c (the coefficients of the quadratic equation in standard form). So, the vertex of the parabola is (3, -2). If we substitute this into the quadratic, we can find y: Taking the average gives us (2 + 4) / 2 = 3. Let’s convert it to factored form and find the vertex that way: Let’s say we have the following quadratic equation in standard form: Example: How To Find The Vertex Of A Parabola From An Equation In Standard Form So, the coordinates of the vertex are (-b / 2a, c – (b 2 / 4a)). This gives us a y-coordinate of c – (b 2 / 4a) for the vertex of the parabola. We can then substitute x = -b/2a into the quadratic equation to find the value of y. Then the vertex has an x-coordinate of –b/2a. We also have the option of using the shortcut formula for the vertex of a parabola in standard form. To find the vertex of a parabola in standard form, we can convert to either vertex form or factored form and then follow the steps in the previous examples. How To Find The Vertex Of A Parabola In Standard Form We get the same answer for the vertex: (5, -36). Note: we can also convert the quadratic equation to vertex form and then read the coordinates as in the last example: The parabola y = 24(x – 2)(x – 8) has its vertex at the point (5, -36). Step 4: The vertex of the parabola is the point (h, k) = (5, -36). So, k = -36 is the y-coordinate of the vertex. Step 3: We substitute x = 5 into the quadratic equation to get 4(5 – 2)(5 – 8) = 4(3)(-3) = -36. So, h = 5 is the x-coordinate of the vertex. Step 2: The average of r = 2 and s = 8 is (2 + 8) / 2 = 5. Step 1: In this case, r = 2 and s = 8 are the two zeros (roots) of this quadratic equation. Let’s say we have the following quadratic equation in factored form: Example: How To Find The Vertex Of A Parabola From An Equation In Factored Form This will always give us a y-coordinate of k = -a(r – s) 2 / 4