Question

Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros.

Answer 1

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: brainly.com/question/4074088

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