For the points in the parabola, we have:
- A = (1, 0)
- B = (3, 0)
- P = (0, 3)
- Q = (2, -1).
How to identify the points on the parabola?
Here we have the quadratic equation:
y = (x - 1)*(x - 3)
First, we want the coordinates of A and B, which are the two zeros of the parabola.
Because it is already factorized, we know that the zeros are at x = 1 and x = 3, so the coordinates of A and B are:
A = (1, 0)
B = (3, 0).
Then point P is the y-intercept, to get it, we need to evaluate in x = 0.
y = (0 - 1)*(0 - 3) = (-1)*(-3) = 3
Then we have:
P = (0, 3)
Finally, point Q is the vertex. The x-value of the vertex is in the middle between the two zeros, so the vertex is at x = 2.
And the y-value of the vertex is:
y = (2 - 1)*(2 - 3) = 1*(-1) = -1
So we have:
Q = (2, -1).
If you want to learn more about quadratic equations:
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