Step-by-step explanation:
This equation is written in standard form, y = ax² + bx + c.
a = 1 , b = -2 , c = -4
First, the x² tells you that this is going to be a parabola. Since the a is positive, the parabola will be facing up (with the ends pointing up).
Next, you find the axis of symmetry, or vertex, which is where the middle of the parabola is. The formula for this is [tex]\frac{-b}{2a}[/tex].
[tex]\frac{-(-2)}{2(1)}[/tex] Simplify
[tex]\frac{2}{2}[/tex] Simplify
1
So, the middle of your parabola will be at x = 1.
Now, find the x-intercept. Since the x-intercept of a graph is where y = 0, just plug 0 into the equation for y.
y = x² - 2x - 4 Plug in 0
0 = x² - 2x - 4 Factoring won't work, so use the Quadratic Formula.
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex] Plug in[tex]$x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-4)}}{2(1)}$[/tex] Simplify
[tex]$x=\frac{2\pm\sqrt{4+16}}{2}$[/tex] Simplify
[tex]$x=\frac{2\pm\sqrt{20}}{2}$[/tex] The square root of 20 is about 4.47.
[tex]$x=\frac{2+4.47}{2}$[/tex] and [tex]$x=\frac{2-4.47}{2}$[/tex] Simplify
x = 3.235 and -1.235
These are your x-intercepts, where your parabola crosses the x-axis.
Now, just put all of this information together on a graph!
