With this, the vertex has the x-coordinate of 1. Knowing this, we can substitute 'b' with 2 and substitute 'a' with -1. Hence, we can see that, 'a' is equals to -1, ‘b’ is equals to 2, and 'c' is equals to 0. To find the values of 'a' and 'b', we can compare this equation with the general equation, y = ax^2 + bx +c.įor easier comparison, we can rewrite this quadratic equation as, y = -1x^2 +4x + 0. Let's find the coordinates of this vertex.Īgain, we start with the formula for the x-coordinate of the vertex of a quadratic equation, x = -b/2a. Now, the vertex is located at the highest point on the graph. The graph for this equation is shown here. Consider the quadratic equation, y = -x^2 +2x. Hence, the vertex of the equation has the coordinates of (2, -5). Hence, the vertex has y-coordinate of -5. Adding -16 with 3, gives -13.Īgain, we can substitute x with 2. Now, we can use the x–coordinate to find the y-coordinate of the vertex. With this, we know that the vertex of the quadratic equation has the x-coordinate of 2. 8 divide by 4, gives 2įinally, we have x equals to 2. Knowing this, we can substitute 'b', with -8, and substitute 'a', with 2. To find out the values of 'a', 'b' and 'c', we can rewrite this equation as, y = 2x^2 + (-8)x +3.īy comparing this equation with the general equation, we can see that, 'a' is equals to 2, 'b' is equals to -8, and 'c' is equals to 3. Let's see an example on using this formula, by using this equation, y = 2x^2 -8x +3. Where, 'a', 'b' and 'c' are the coefficients for each term respectively. The general equation of a quadratic equation is given as, y = ax^2 +bx, +c. Now, what are 'a' and 'b'? Let's find out. Now, there is a formula to calculate the x-coordinate of the vertex of a quadratic equation. Hence, this point is the vertex of a quadratic equation.Īlso, if you have a quadratic graph as shown here, the lowest point, is also the vertex of the quadratic equation, y = 2x^2 -8x +3. Notice that, this is the highest point on the graph. Now, this is the graph of the quadratic equation, y= -x^2 +2x. In this lesson, we will learn about the vertex of a quadratic equation.