The direction of the parabola is determined by the leading coefficient of the polynomial (a > 0 - Upwards, a < 0 - Downwards). The y-intercept of the polynomial is c and the two zeros of the polynomial are x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c).
What are the characteristics of quadratic equations?
Herein we have a quadratic equation of the form f(x) = a · x² + b · x + c. To determine the direction of the parabola, we must transform this expression into its vertex form and looking for the sign of the vertex constant:
f(x) = a · x² + b · x + c
f(x) = a · [x² + (b / a) · x + (c / a)]
f(x) + b² / (4 · a) - c = a · [x² + (b / a) · x + b² / (4 · a²)]
f(x) + b² / (4 · a) - c = a · [x + b / (2 · a)]²
If a > 0, then the direction of the parabola is upwards, but if a < 0, then the direction of the parabola is downwards.
The y-intercept is found by evaluating the quadratic equation at x = 0:
f(0) = a · 0² + b · 0 + c
f(0) = c
And the zeros are determined by the quadratic formula:
x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c)
The direction of the parabola is determined by the leading coefficient of the polynomial (a > 0 - Upwards, a < 0 - Downwards). The y-intercept of the polynomial is c and the two zeros of the polynomial are x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c).
To learn more on parabolas: https://brainly.com/question/4074088
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