Case A - The coefficients of the quadratic equation are a = 2, b = 4 and c = - 26.
Case B - The quadratic equation has the following turning point: (x, y) = (- 4, - 26).
How to find the real coefficients associated with a quadratic equation
Case A - In this problem we find a quadratic equation in standard form, whose coefficients must be found by obtaining vertex form and comparing terms. This can be done by algebra properties. First, write the entire equation:
2 · x² + 16 · x + 6
Second, find the vertex form of the quadratic equation:
2 · (x² + 8 · x) + 6
2 · (x² + 8 · x + 16) - 2 · 16 + 6
2 · (x + 4)² - 26
The values of the coefficients are a = 2, b = 4 and c = - 26.
Case B - The turning point of the quadratic equation is the vertex, which can be extracted from the vertex form thereof:
y = 2 · x² + 16 · x + 6
y = 2 · (x² + 8 · x + 3)
y + 2 · 13 = 2 · (x² + 8 · x + 16)
y + 26 = 2 · (x + 4)²
The turning point of the quadratic equation is (x, y) = (- 4, - 26).