Question
what is the vertex form of the graphed equation? (coordinates are (-4, -2)
y = - (x - ___)^2+ ___
y = - (x - ___)^2+ ___
Answers
GPT-4o mini
To convert the vertex form of a quadratic equation, which is given by:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola, we can use the provided vertex coordinates.
Given the vertex coordinates are \((-4, -2)\), we can identify \(h\) and \(k\):
- \(h = -4\)
- \(k = -2\)
Since the parabola opens downward (indicated by the negative sign in front of the quadratic term), we have \(a < 0\). We'll use \(a = -1\) for simplicity unless specified otherwise.
Now substituting these values into the vertex form:
\[ y = -1(x - (-4))^2 - 2 \]
This simplifies to:
\[ y = -1(x + 4)^2 - 2 \]
So, filling in the blanks in the equation you provided, we have:
\[ y = - (x - (-4))^2 - 2 \]
Thus, the complete vertex form is:
\[ y = - (x + 4)^2 - 2 \]
The values to fill in the blanks are:
1. The first blank is \( -4\) (which makes \(x - (-4)\) become \(x + 4\)).
2. The second blank is \( -2\).
So:
y = - (x - (-4))^2 + (-2)
Would give you the vertex form.
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola, we can use the provided vertex coordinates.
Given the vertex coordinates are \((-4, -2)\), we can identify \(h\) and \(k\):
- \(h = -4\)
- \(k = -2\)
Since the parabola opens downward (indicated by the negative sign in front of the quadratic term), we have \(a < 0\). We'll use \(a = -1\) for simplicity unless specified otherwise.
Now substituting these values into the vertex form:
\[ y = -1(x - (-4))^2 - 2 \]
This simplifies to:
\[ y = -1(x + 4)^2 - 2 \]
So, filling in the blanks in the equation you provided, we have:
\[ y = - (x - (-4))^2 - 2 \]
Thus, the complete vertex form is:
\[ y = - (x + 4)^2 - 2 \]
The values to fill in the blanks are:
1. The first blank is \( -4\) (which makes \(x - (-4)\) become \(x + 4\)).
2. The second blank is \( -2\).
So:
y = - (x - (-4))^2 + (-2)
Would give you the vertex form.