The quadratic equation has the following results: (p, q) = (8, 15), minimum point: (h, k) = (1, 4), range of values: - 4 < x < - 3
How to analyze quadratic equations
In this question we have a quadratic equation of the form y = x² + p · x + q , whose missing coefficients can be found by solving on the following system of linear equations:
- 5 · p + q = - 25
- 3 · p + q = - 9
(p, q) = (8, 15)
The vertex represents the minimum point, which is found by changing the form of the equation from standard form into vertex form:
y = x² + 8 · x + 15
y + 1 = x² + 8 · x + 16
y + 1 = (x + 4)²
(h, k) = (1, 4)
And lastly we must solve for x in the following inequality:
x² + 8 · x + 15 < x + 3
x² + 7 · x + 12 < 0
(x + 3) · (x + 4) < 0
- 4 < x < - 3
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