Use any method to locate the zeros of y = -3x^2 +12x + 15.
• (1,0) (-5,0)
• There are no zeros
• (0,15)
• (-1,0) (5,0)
To find the zeros of the equation y = -3x^2 + 12x + 15, we need to set y equal to zero and solve for x.
Setting y = 0, we get:
0 = -3x^2 + 12x + 15
Rearranging the equation, we have:
3x^2 - 12x - 15 = 0
Now we can factor the quadratic equation. Taking out a common factor of 3, we get:
3(x^2 - 4x - 5) = 0
Next, we can factor the quadratic expression in the parentheses:
3(x - 5)(x + 1) = 0
Now we have factored form, where each factor can be set equal to zero:
x - 5 = 0 or x + 1 = 0
Solving each equation, we find:
x = 5 or x = -1
Therefore, the zeros of the equation y = -3x^2 + 12x + 15 are (5, 0) and (-1, 0).
To locate the zeros of the quadratic equation y = -3x^2 + 12x + 15, we need to set y equal to zero and solve for x.
So, we have:
-3x^2 + 12x + 15 = 0
Now, we can use different methods to find the zeros. Let's use the quadratic formula.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = -3, b = 12, and c = 15. Substituting these values into the quadratic formula, we have:
x = (-12 ± √(12^2 - 4(-3)(15))) / (2(-3))
x = (-12 ± √(144 + 180)) / (-6)
x = (-12 ± √324) / (-6)
x = (-12 ± 18) / (-6)
Now we have two possible solutions:
1. x = (-12 + 18) / (-6) = 6 / -6 = -1
2. x = (-12 - 18) / (-6) = -30 / -6 = 5
Therefore, the zeros of the equation y = -3x^2 + 12x + 15 are x = -1 and x = 5. Thus, the correct option is (C) (-1,0) (5,0).
To locate the zeros of the quadratic function y = -3x^2 +12x + 15, we need to find the values of x for which y equals zero.
Method 1: Factoring
To find the zeros through factoring, we need to rewrite the equation in factored form. We start by setting y = 0:
0 = -3x^2 + 12x + 15
Next, we factor out any common factors from the three terms:
0 = -3(x^2 - 4x - 5)
To factor the quadratic expression inside the parentheses, we look for two numbers whose product is -5 and whose sum is -4. The numbers are -5 and 1, so we rewrite the equation as:
0 = -3(x - 5)(x + 1)
Now, we can set each factor equal to zero and solve for x:
x - 5 = 0 --> x = 5
x + 1 = 0 --> x = -1
Therefore, the zeros of the function y = -3x^2 +12x + 15 are x = -1 and x = 5.
Method 2: Quadratic Formula
Another method to find the zeros is by using the quadratic formula. The quadratic formula states that for a quadratic equation of the form ax^2 + bx + c = 0, the zeros can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation y = -3x^2 + 12x + 15, we have a = -3, b = 12, and c = 15. Substituting 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)
This gives us two possible solutions:
x = (-12 + 18) / (-6) = 6 / (-6) = -1
x = (-12 - 18) / (-6) = -30 / (-6) = 5
So, the zeros of the function y = -3x^2 +12x + 15 are x = -1 and x = 5.
Comparing the options:
• (1,0) (-5,0): This is not correct because the zeros are x = -1 and x = 5, not x = 1 and x = -5.
• There are no zeros: This is not correct because, as we found, the function has two zeros at x = -1 and x = 5.
• (0,15): This is not correct because the point (0,15) is not a zero of the function.
• (-1,0) (5,0): This is the correct answer because the zeros of the function are x = -1 and x = 5.