Which of the following quadratic functions has zeros at x = -3 and x = 2?
y=(x+3)(x-2)
y=(x-3)(x+2)
y=(x+3)^2-2
y=(x-3)^2+2
Y = (x+3)(x-2) = 0.
x+3 = 0. x = -3.
x-2 = 0. x = 2.
So the ans. is a.
Well, let me do some calculations on my imaginary calculator... *beep boop beep boop*
Alright, after some clown math, it looks like the correct answer is:
y=(x+3)(x-2)
Because when you plug in x = -3 and x = 2, it makes the whole equation equal to zero. Those zeros are like magic, making everything disappear! Just like my career aspirations. *ba dum tss*
To find the quadratic function that has zeros at x = -3 and x = 2, we need to use the factored form of a quadratic equation.
The factored form of a quadratic equation is given as y = a(x - r)(x - s), where r and s are the zeros of the equation.
In this case, the zeros are -3 and 2, so one possible quadratic function is:
y = (x + 3)(x - 2)
Therefore, the correct answer is:
y = (x + 3)(x - 2)
To find the quadratic function with zeros at x = -3 and x = 2, we need to identify the equation that produces these values when set to zero.
Let's go through each option and test them out:
1. y = (x + 3)(x - 2)
To find the zeros, we set y = 0 and solve the equation:
0 = (x + 3)(x - 2)
Setting each factor to zero:
x + 3 = 0 or x - 2 = 0
x = -3 or x = 2
This option has the correct zeros at x = -3 and x = 2.
2. y = (x - 3)(x + 2)
Again, let's set y = 0 and solve the equation:
0 = (x - 3)(x + 2)
Setting each factor to zero:
x - 3 = 0 or x + 2 = 0
x = 3 or x = -2
This option does not have the correct zeros, so it is not the answer.
3. y = (x + 3)^2 - 2
Let's set y = 0 and solve the equation:
0 = (x + 3)^2 - 2
(x + 3)^2 - 2 = 0
(x + 3)^2 = 2
(x + 3) = √2 or (x + 3) = -√2
x = √2 - 3 or x = -√2 - 3
This option does not have the correct zeros, so it is not the answer.
4. y = (x - 3)^2 + 2
Setting y = 0 and solving the equation:
0 = (x - 3)^2 + 2
(x - 3)^2 = -2
This equation is not possible since the square of any real number cannot be negative. So, this option does not have any zeros.
Therefore, the quadratic function that has zeros at x = -3 and x = 2 is y = (x + 3)(x - 2). Option 1 is the correct answer.