Question

Given the following parabolas

y = 12x² + 14x - 4
Identify the following points
1) The roots
2) The y-intercept
3) The vertex
4) The value at x = 3.3
5) The value at x = -1.8

Answer 1

To answer the student's question regarding a quadratic equation, we would find the roots using the quadratic formula, the y-intercept by setting x to zero, the vertex using the vertex formula, and the value at specific points by plugging those x-values into the equation.

Step-by-step explanation:

The given equation y = 12x² + 14x - 4 represents a quadratic equation that can be written in the general form at² + bt + c = 0. To find the points requested, one would typically use the quadratic formula, vertex formula, and substituting values for x.

• The roots can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients from the equation.
• The y-intercept is the point where x=0. By substituting x into the equation, we get the y-intercept.
• The vertex of the parabola can be found using the formula x = -b / (2a) to find the x-coordinate, and then substituting this value back into the equation to find the corresponding y-coordinate.
• The value at x = 3.3 is found by substituting 3.3 for x in the equation and calculating y.
• The value at x = -1.8 is obtained by substituting -1.8 for x in the equation and solving for y.

Note that to identify the actual numerical answers to these points, calculations using the specific coefficients provided in the equation must be performed.