Find the intersection points of the function with the coordinate axes: y = -x² + 4x-3.

| April 30, 2021 | education

We need to find the points of intersection of the graph of the function with the coordinate axes. Function y = – x ^ 2 + 4x – 3.
In order to find the value of the points of intersection of the graph of the function with the OX axis, we must solve the equation at y = 0.
So, we get the quadratic equation: – x ^ 2 + 4x – 3 = 0; Multiply both sides of the equation by -1.
x ^ 2 – 4x + 3 = 0.
We are looking for the discriminant:
D = b ^ 2 – 4ac = (-4) ^ 2 – 4 * 1 * 3 = 16 – 12 = 4.
We are looking for the roots of the equation:
x1 = (-b + √D) / 2a = (4 + 2) / 2 = 6/2 = 3.
x2 = (-b – √D) / 2a = (4 – 2) / 2 = 2/2 = 1.
Intersection points about the x-axis: (3; 0) and (1; 0).
In order to find the value of the points of intersection of the graph of the function with the axis of the OY, we must solve the equation at x = 0. We get, y = -3.
Y-intercept: (0; -3).



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