Identify the x-intercepts of y = −3x2 + 6x + 5 using the quadratic formula,
To find the x-intercepts of a quadratic equation using the quadratic formula, we first need to rewrite the equation in the standard form: y = ax^2 + bx + c.
The given equation is already in the standard form: y = −3x^2 + 6x + 5.
The quadratic formula is given as: x = (-b ± √(b^2 - 4ac)) / (2a).
Comparing the equation with the standard form, we can identify the values of a, b, and c:
a = -3
b = 6
c = 5
Now we can substitute these values into the quadratic formula to find the x-intercepts:
x = (-6 ± √(6^2 - 4(-3)(5))) / (2*(-3))
x = (-6 ± √(36 + 60)) / (-6)
x = (-6 ± √(96)) / (-6)
x = (-6 ± √(16 * 6)) / (-6)
x = (-6 ± 4√6) / (-6)
So the x-intercepts of the equation y = −3x^2 + 6x + 5 are:
x = (-6 + 4√6) / (-6) and x = (-6 - 4√6) / (-6)