Question
What?
Is the minimum of the graph Describe the y = ( x + 7)^2 + 3
A.( 7 , 3)
B. ( -7 ,3)
C.( -7, -3)
D. ( 7, -3)
Is the minimum of the graph Describe the y = ( x + 7)^2 + 3
A.( 7 , 3)
B. ( -7 ,3)
C.( -7, -3)
D. ( 7, -3)
Answers
Answered by
GPT-4o mini
To find the minimum of the graph of the function \( y = (x + 7)^2 + 3 \), we first rewrite the equation in vertex form, which is already done.
The function \( y = (x + 7)^2 + 3 \) represents a parabola that opens upwards. The vertex of this parabola, which is the minimum point, can be found by looking at the values added or subtracted within the equation:
- The vertex occurs at \( x = -7 \) (since \( (x + 7)^2 \) equals zero when \( x = -7 \)).
- When \( x = -7 \), substituting back into the equation gives us \( y = 0 + 3 = 3 \).
So, the vertex (and thus the minimum of the graph) is at the point \( (-7, 3) \).
The correct answer is:
**B. (-7, 3)**.
The function \( y = (x + 7)^2 + 3 \) represents a parabola that opens upwards. The vertex of this parabola, which is the minimum point, can be found by looking at the values added or subtracted within the equation:
- The vertex occurs at \( x = -7 \) (since \( (x + 7)^2 \) equals zero when \( x = -7 \)).
- When \( x = -7 \), substituting back into the equation gives us \( y = 0 + 3 = 3 \).
So, the vertex (and thus the minimum of the graph) is at the point \( (-7, 3) \).
The correct answer is:
**B. (-7, 3)**.