Question
Features of Graphs of Quadratic Equations Quick Check
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Question
Use any method to locate the zeros of y=−3x2+12x+15.(1 point)
Responses
(0,15)
left parenthesis 0 comma 15 right parenthesis
There are no zeros.
There are no zeros.
(−1,0)(5,0)
left parenthesis negative 1 comma 0 right parenthesis left parenthesis 5 comma 0 right parenthesis
(1,0)(−5,0)
left parenthesis 1 comma 0 right parenthesis left parenthesis negative 5 comma 0 right parenthesis
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Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the zeros of the quadratic equation \( y = -3x^2 + 12x + 15 \), we can set the equation to zero and solve for \( x \):
\[
-3x^2 + 12x + 15 = 0
\]
To simplify the equation, we can divide everything by -3:
\[
x^2 - 4x - 5 = 0
\]
Next, we can factor the quadratic:
\[
(x - 5)(x + 1) = 0
\]
Setting each factor to zero gives us the possible solutions:
\[
x - 5 = 0 \quad \Rightarrow \quad x = 5
\]
\[
x + 1 = 0 \quad \Rightarrow \quad x = -1
\]
Thus, the zeros of the quadratic equation are \( x = 5 \) and \( x = -1 \).
In coordinate notation, the zeros are:
\[
(-1, 0) \quad \text{and} \quad (5, 0)
\]
Therefore, the correct response would be:
**(−1, 0) and (5, 0)**.
\[
-3x^2 + 12x + 15 = 0
\]
To simplify the equation, we can divide everything by -3:
\[
x^2 - 4x - 5 = 0
\]
Next, we can factor the quadratic:
\[
(x - 5)(x + 1) = 0
\]
Setting each factor to zero gives us the possible solutions:
\[
x - 5 = 0 \quad \Rightarrow \quad x = 5
\]
\[
x + 1 = 0 \quad \Rightarrow \quad x = -1
\]
Thus, the zeros of the quadratic equation are \( x = 5 \) and \( x = -1 \).
In coordinate notation, the zeros are:
\[
(-1, 0) \quad \text{and} \quad (5, 0)
\]
Therefore, the correct response would be:
**(−1, 0) and (5, 0)**.
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