If the x-intercepts are given, it is easier to write the equation in intercept form. Conversely, if the vertex is given, it is easier to write the equation in vertex form.
Practice makes perfect
If the x-intercepts are given, it is easier to write the equation in intercept form. Conversely, if the vertex is given, it is easier to write the equation in vertex form. Let's see two examples.
Example 1
Let's suppose the x-intercepts of a parabola are 1 and 3, and it passes through the point (0,6). What is the equation of the quadratic function? In this case, since we know the x-intercepts, it is easier to use the intercept form.
y=a(x-p)(x-q)
In the above formula, p and q are the x-intercepts. Therefore, we have that p=1 and q= 3.
y=a(x-1)(x- 3)Finally, to find the value of a, we will use the fact that the parabola passes through the point (0,6). Let's substitute 0 and 6 for x and y, respectively, in the above formula.
Now that we know that a=2, we can write the full equation.
y=2(x-1)(x-3)
We can graph the function to see the intercepts and the point.
Example 2
Let's suppose (5,2) is the vertex of a parabola which also passes through the point (1,10). Since we know the coordinates of the vertex, we will use the vertex form.
y=a(x-h)^2+k
In the above formula, h and k are the x- and y-coordinates of the vertex, respectively. Therefore, h=5 and k= 2.
y=a(x-5)^2+ 2
Finally, to find the value of a, we will use the fact that the parabola passes through the point (1,10). Let's substitute 1 and 10 for x and y, respectively, in the above formula.
