f(x)= -4(x+5)^2+3
The vertex is : -5,3
The line of symmetry is x= 3
The maximum/minimum value of f(x)= -5
Is the value of f(-5)=3, a minimum or maximum? Minimum
Graphing would open from the bottom going up on the negative side.
write your vertex as (-5,3)
the line of symmetry is the x of the vertex, so
line of symmetry is x = -5
the max of the function is 3, (the y value of the vertex)
since the value of "a" of your function is negative, the parabola opens downwards, thus a Maximum.
Okay. I had the vertex written in correctly. the line of symmetry & max function I had backwards for some unknown reason. The other 2 parts I had totally wrong.
Thank you for checking this for me Reiny! I was leery at posting it until I had it checked. Good thing I did!
I put the vertex as (-5,3) and it is saying it was wrong...ughhhhhhhh.
the vertex is indeed (-5,3)
For
f(x)=a(x-h)+k, the vertex is at:
(h,k).
Since the function is already in that form, where
a=-4,
h=-5, and
k=3
f(x)= -4(x+5)^2+3
as Mr. Pursley stated:
"the vertex is indeed at (-5,3)".
Reread the question to see if
1. there are errors of transcription, especially signs
2. there are instructions on the format of presentation of answers.
There are times (but rare) that the computer rejects the correct answers. Hope this is not one of them.
To determine the vertex of a quadratic equation in the form f(x) = ax^2 + bx + c, the vertex formula is used. The vertex formula is given by (-b/2a, f(-b/2a)).
In this equation, f(x) = -4(x + 5)^2 + 3, the a value is -4, the b value is 0, and the c value is 3. Therefore, the vertex formula becomes (-0/2(-4), f(-0/2(-4))) = (-0/0, f(0)).
Simplifying further, the vertex formula becomes (0, f(0)). Evaluating f(0) in the equation f(x) = -4(x + 5)^2 + 3, we get f(0) = -4(0 + 5)^2 + 3 = -100 + 3 = -97. Hence, the vertex is (0, -97).
To find the line of symmetry, we use the x-coordinate of the vertex. In this case, the line of symmetry is x = 0.
The maximum/minimum value of f(x) can be determined by looking at the coefficient of the x^2 term. Since the coefficient is negative (-4), the graph opens downward, and the function has a maximum value. In this case, the maximum value is f(-5) = 3, which means that the highest point on the graph is at the x-coordinate of -5 and the y-coordinate of 3.
Therefore, the value of f(-5) = 3 represents a minimum point of the graph.