Use any method to locate the zeros of y = -3x^2 + 12x + 15.
A. (1, 0) (-5, 0)
B. (-1, 0) (5, 0)
C. There are no zeros.
D. (0, 15)
To find the zeros of the quadratic function y = -3x^2 + 12x + 15, we need to solve the equation -3x^2 + 12x + 15 = 0.
We can start by factoring out a common factor of -3: -3(x^2 - 4x - 5) = 0.
Next, we can factor the quadratic expression inside the parentheses: (x - 5)(x + 1) = 0.
Finally, we set each factor equal to zero and solve for x:
x - 5 = 0 or x + 1 = 0.
Solving each equation gives us:
x = 5 or x = -1.
Therefore, the zeros of the quadratic function y = -3x^2 + 12x + 15 are x = 5 and x = -1.
Since neither (1,0) nor (-5,0) are the correct solutions, the correct answer is C. There are no zeros.
To locate the zeros of the quadratic function y = -3x^2 + 12x + 15, we can set y equal to zero and solve for x:
0 = -3x^2 + 12x + 15
To solve this quadratic equation, we can factor it, complete the square, or use the quadratic formula. In this case, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
From the equation y = -3x^2 + 12x + 15, we can see that a = -3, b = 12, and c = 15. Plugging these values into the quadratic formula, we get:
x = (-12 ± √(12^2 - 4(-3)(15))) / (2(-3))
x = (-12 ± √(144 + 180)) / (-6)
x = (-12 ± √324) / (-6)
x = (-12 ± 18) / (-6)
Simplifying further:
x = (-12 + 18) / (-6) or x = (-12 - 18) / (-6)
x = 6 / (-6) or x = -30 / (-6)
x = -1 or x = 5
Therefore, the zeros of the function y = -3x^2 + 12x + 15 are x = -1 and x = 5.
The correct answer is:
B. (-1, 0) (5, 0)
To find the zeros of the quadratic equation y = -3x^2 + 12x + 15, we need to determine the values of x that make y equal to zero.
We can start by setting y equal to zero and solving the equation for x:
0 = -3x^2 + 12x + 15
To simplify the equation, we can divide the entire equation by -3 to get:
0 = x^2 - 4x - 5
Now, we can factorize the quadratic equation:
0 = (x - 5)(x + 1)
Setting each factor equal to zero, we get:
x - 5 = 0 or x + 1 = 0
Solving these equations gives us the zeros:
x = 5 or x = -1
Therefore, the zeros of the equation y = -3x^2 + 12x + 15 are x = 5 and x = -1.
So, the correct answer is B. (-1, 0) (5, 0)