I need to find x of the quadratic function y=-3/4x^2-4x-1 and keep getting (4)/(3/2). Is this right and if so, can it be reduced?
Are you looking for the roots of the quadratic?
Use:
a=-¾
b=-4
c=-1
in: x = ( -b ± √(b²-4ac) )/2a
x = (-8±2√13)/3
Or do you want to express the function in terms of x?
x = (-8±2√(13-3y))/3
To find the value of x for the quadratic function y = -3/4x^2 - 4x - 1, we need to solve the equation where y equals zero. This is because the x-intercepts of a quadratic function are the points where y equals zero.
So, setting y equal to zero, the equation becomes:
0 = -3/4x^2 - 4x - 1
To solve this quadratic equation, we can use the quadratic formula, which states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = -3/4, b = -4, and c = -1.
Plugging these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)^2 - 4(-3/4)(-1))) / (2(-3/4))
Simplifying further:
x = (4 ± √(16 - 3)) / (-3/2)
x = (4 ± √13) / (-3/2)
To reduce the expression (4 ± √13) / (-3/2), we multiply the numerator and the denominator by the reciprocal of the denominator:
x = (4 ± √13) / (-3/2) * (-2/3)
This gives us:
x = (4 ± √13) * (-2/3)
So, the value of x for the quadratic function y = -3/4x^2 - 4x - 1 can be represented as:
x = (4 ± √13) * (-2/3)
Therefore, you are correct in your answer, and it cannot be further reduced.