What is y equals 2x2 plus 5x-3?

Answer 1

It is the equation of a quadratic function that happens to factor very nicely:

y = 2x2 + 5x - 3 = (x + 3)(2x - 1).

When the product of two numbers equals zero, then one or other of them must equal zero.

Therefore, when y = 0, one of the two factors must also equal zero:

Hence, either x = -3 or x = ½, when y = 0.

This implies that the graph of this function crosses the x-axis at two places: namely, at (0,-3) and at (0,½).

As the graph of every quadratic function is a parabola, its axis of symmetry is the vertical line passing through the point on the x-axis that is mid-way betwixt the two points named above, where the function crosses the x-axis: namely, at (0,-1¼).

To find the vertex of the above parabola, we solve for y where x = -1¼:

y = (x + 3)(2x - 1)

= (-1¼ + 3)(-1¼ - 1)

= (1¾)(-2¼)

= (7/4)(-9/4) = 63/16 = 3 15/16

-3;

hence, the vertex is located at the point, (-1¼,315/16).