Use factoring to identify the x-intercepts of y = 4x^2 + 8x − 5.
To identify the x-intercepts of the equation y = 4x^2 + 8x - 5 using factoring, we need to find the values of x when y equals zero.
So, we set y = 0:
0 = 4x^2 + 8x - 5
Now, let's factor the quadratic equation. The easiest way to do this is to find two numbers that multiply to give -20 (4* -5), and also add up to give 8.
The numbers that satisfy these conditions are +10 and -2.
Therefore, we can rewrite the equation as:
0 = (2x + 5)(2x - 1)
Now, we set each factor equal to zero and solve for x:
2x + 5 = 0 or 2x - 1 = 0
2x = -5 or 2x = 1
x = -5/2 or x = 1/2
Therefore, the x-intercepts of the equation y = 4x^2 + 8x - 5 are -5/2 and 1/2.