The equation f (x ) = -6x2– 24x + 72 representsa quadratic function.What is the value of the positive zero of the function?
A. 2
B. 4
C. 6
D. 8
To find the positive zero of a quadratic function, we need to find the value of x when f(x) equals zero.
So, let's set f(x) equal to zero and solve for x:
-6x^2 - 24x + 72 = 0
Divide every term by -6 to simplify the equation:
x^2 + 4x - 12 = 0
To factor this quadratic equation, we need to find two numbers whose product is -12 and whose sum is 4.
The factors of -12 are -1 and 12, -2 and 6, and -3 and 4.
The sum 4 can be obtained by adding -2 and 6, so we can write the equation as:
(x - 2)(x + 6) = 0
Setting each factor equal to zero gives us:
x - 2 = 0 or x + 6 = 0
Solving these equations, we get:
x = 2 or x = -6
Since we are looking for the positive zero, the answer is:
A. 2
To find the positive zero of the function, we need to find the value of x where the function f(x) equals zero. In other words, we need to solve the equation -6x^2 - 24x + 72 = 0.
One way to solve this equation is by factoring. However, in this case, the equation does not easily factor into two binomials. So, we can use the quadratic formula to find the solutions.
The quadratic formula states that for an 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 equation, a = -6, b = -24, and c = 72. Plugging these values into the quadratic formula, we get:
x = (-(-24) ± √((-24)^2 - 4(-6)(72))) / (2(-6))
= (24 ± √(576 + 1728)) / -12
= (24 ± √2304) / -12
= (24 ± 48) / -12
Simplifying further, we have:
x = (24 + 48) / -12 = 72 / -12 = -6
x = (24 - 48) / -12 = -24 / -12 = 2
So the solutions are x = -6 and x = 2. However, we are only interested in the positive zero. Therefore, the answer is A. 2.
-3 x^2 - 12 x + 36 = 0
- x^2 - 4 x + 12 = 0
x^2 + 4 x - 12 = 0
(x+6)(x-2) = 0
x = +2 or -6