how do i graph this quadratic funtion
y=x(squared) + 4x - 4
To graph the quadratic function y = x^2 + 4x - 4, you can follow these steps:
Step 1: Determine the vertex of the parabola.
a) The x-coordinate of the vertex can be found using the formula: x = -b / (2a), where a is the coefficient of x^2 and b is the coefficient of x. In this case, a = 1 and b = 4.
x = -4 / (2 * 1) = -2
b) To find the y-coordinate of the vertex, substitute the x-coordinate back into the original equation.
y = (-2)^2 + 4(-2) - 4 = 4 - 8 - 4 = -8
So, the vertex is (-2, -8).
Step 2: Determine the y-intercept.
The y-intercept is the value of y when x is zero. Plug in x = 0 into the equation:
y = (0)^2 + 4(0) - 4 = 0 + 0 - 4 = -4
So, the y-intercept is (0, -4).
Step 3: Find the x-intercepts.
To find the x-intercepts, set y = 0 and solve for x.
0 = x^2 + 4x - 4
This quadratic equation can be factored or solved using the quadratic formula.
Using factoring:
0 = (x - 1)(x + 4)
So, the x-intercepts are x = 1 and x = -4.
Step 4: Plot the points and draw the parabola.
Now that we have the vertex, y-intercept, and x-intercepts, we can plot these points on a graph and sketch the parabola. Start by plotting the vertex (-2, -8), the y-intercept (0, -4), and the x-intercepts (1, 0) and (-4, 0). Then, draw a smooth curve that passes through these points symmetrically.
The graph should look like a U-shaped curve opening upwards, with the vertex as the lowest point.