What is the graph of y equals x2 5x-4?

Answer 1

Any quadratic expression describes a parabola. We can find the exact details of it by observing and manipulating the equation:

y = x2 + 5x - 4

The fact that the squared term has a positive coefficient tells us that the parabola extends infintely upwards on a graph.

To find the bottom most point on the parabola, we can take it's derivative and solve for 0:

dy/dx = 2x + 5

0 = 2x + 5

x = -5/2

The y-coordinate can be found by plugging that value into the original equation:

y = (-5/2)2 + 5(-5/2) - 4

y = 25/4 - 25/2 - 4

y = -25/4 - 16/4

y = -41/4

If you want to find where it intersects the x-axis, you can do so by solving the original equation for zero:

y = x2 + 5x - 4

x2 + 5x - 4 = 0

x2 + 5x + (5/2)2 = 4 + (5/2)2

(x + 5/2)2 = 4 + 25/4

x + 5/2 = ±√[(16 + 25)/4]

x = -5/2 ±√41 / 2

x = (-5 ± √41) / 2

If you want to find another pair of points on the graph, allowing you to roughly sketch the parabola in question, you can do so by assigning another value to y and solving it for x. As long as the result doesn't give you any complex numbers, then you can plot it on the graph giving you a fourth and fifth point with which to plot.