Use factoring to identify the x-intercepts of y = −5x^2 − x + 4.
To identify the x-intercepts of the quadratic equation y = -5x^2 - x + 4, we need to set y equal to zero and solve for x.
0 = -5x^2 - x + 4
To factor this quadratic equation, we can first multiply both sides by -1 to make the leading coefficient positive:
0 = 5x^2 + x - 4
Now, we need to find two numbers that multiply to 5*-4 = -20 and add up to 1, which is the coefficient of x. These numbers are 5 and -4.
0 = (5x - 4)(x + 1)
Now we can set each factor equal to zero:
5x - 4 = 0
x + 1 = 0
Solving these equations, we find the x-intercepts:
5x = 4
x = 4/5
x = -1
Therefore, the x-intercepts of the equation y = -5x^2 - x + 4 are x = 4/5 and x = -1.