Respuesta :
The quadratic function that has x-intercepts at x = 3, and x = -5 that
passes through the point (1, -12) is f(x) = x² + 2·x - 15.
How can the required quadratic function be found?
The intercepts of the graph of the quadratic function are x = 3 and x = -5
The point through which graph passes is (1, -12)
Required:
The equation of the quadratic function.
Solution:
Given that the intercepts are x = 3, and x = -5, we have;
x = 3, and x = -5 are the zeros of the quadratic function, which gives;
Factors of the quadratic function are; (x - 3) and (x + 5)
From which we have;
(x - 3) × (x + 5) = x² + 2·x - 15 is a factor of the quadratic function
When x = 1, we have;
1² + 2 × 1 - 15 = -12
Therefore, the point (1, -12) is a point on the quadratic function x² + 2·x -
15 that has intercepts at x = 3, and x = -5
The equation of the quadratic function is therefore;
- [tex]\underline{f(x) = x^2 + 2 \cdot x - 15}[/tex]
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