Question

Which graph represents the given equation? A. A parabola declines through (negative 1, 4), (negative 1, 3), (0, 2) and (1 point 5, negative 4 point 5) and rises through (2, negative 4), (3, 0) and (4, 6) on the x y coordinate plane. B. A parabola declines through (negative 4, 5), (negative 3 point 5, 2), (negative 3, 0) and (negative 1 point 5, negative 4 point 5) and rises through (0, negative 2), (1, 3) and (1, 4) on the x y coordinate plane. C. A parabola declines through (negative 2 point 3, 5), (negative 2, 2) and (negative 0 point 5, negative 3 point 1) and rises through (0, negative 2), (1, 4) and (1, 5) on the x y coordinate plane. D. A parabola declines through (negative 1, 5), (negative 0 point 5, 2), (0, negative 2) and (0 point 5, negative 3 point 1) and increases through (2, 2), (2 point 5, 5) on the x y coordinate plane.

Answer 1

The graph of the quadratic function y = 1.5x² + 4x - 2 is given by the image shown at the end of the answer.

How to obtain the graph of a quadratic function?

To obtain the graph of a quadratic function, these three features have to be obtained from the function's definition:

• The x-intercepts, which are the roots of the function.

• The y-intercept, which is the value of y when the function crosses the y-axis.

• The vertex, which is the turning point of the function.

The function for this problem is defined as follows:

y = 1.5x² + 4x - 2.

Hence the numeric values of the coefficients are listed as follows:

a = 1.5, b = 4, c = -2.

Inserting these coefficients into a calculator, the x-intercepts of the function are given as follows:

• x = -3.09  -> hence the function passes through point (-3.09, 0).

• x = 0.43 -> hence the function passes through point (0.43, 0).

The y-intercept of the function is given by coefficient c = -2, hence the function also passes through point (0, -2).

The x-coordinate of the vertex is given as follows:

x = -b/2a = -4/3 = -1.33.

Hence the y-coordinate of the vertex is of:

y = 1.5(-1.33)² + 4(-1.33) - 2 = -4.67.

Missing Information

The problem asks for the graph of the following function:

y = 1.5x² + 4x - 2.

More can be learned about quadratic functions at brainly.com/question/24737967

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