What does x2 + 11x + 24 look like on a graph

The equation x^2 + 11x + 24 looks like this when graphed.

I hope this helps!

To graph a parabola without a calculator, we can factor it to find its root values. These are the x values where the graph is equal to 0 (on the x-axis).

x^2 + 11x + 24 can be factored to:

(x+8)(x+3)

Set both factors equal to 0 to find the roots:

x+8=0
x=-8

x+3=0
x=-3

So the graph crosses the x-axis at x = -8 and x = -3.

Next we can find the vertex of the graph. This is the point where the slope changes directions. Since the x^2 term is positive, we know the parabola is facing up (like a smile face). Therefore the vertex is a minimum value.

We can find the x value of the minima by finding the difference between the roots. Half way from -3 to -8 is -5.5.

Next we can find the y value by plugging -5.5 in for x:

y = (-5.5)^2 + 11(-5.5) + 24 = -6.25

So the vertex is at (-5.5, -6.25)

Note: Minima and maxima can be found easier by using calculus.

From these three points we can draw a pretty accurate graph of the equation. See the attached picture.