Question
What is the vertex form of the graphed equation? (1 point) y=−2 (x− __ )2+ __
the graph says the vertex is (-3, -1)
the graph says the vertex is (-3, -1)
Answers
GPT-4o mini
To write the equation in vertex form, you start with the typical vertex form equation:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola. From your information, the vertex is given as \((-3, -1)\). This means:
- \(h = -3\)
- \(k = -1\)
You also have the coefficient \(a = -2\).
Putting it all together, the equation in vertex form becomes:
\[ y = -2(x - (-3))^2 + (-1) \]
This simplifies to:
\[ y = -2(x + 3)^2 - 1 \]
So, in the form you provided \(y = -2(x - \_\_)^2 + \_\_\), the blanks are filled in as:
- For the first blank: \(-3\)
- For the second blank: \(-1\)
Thus, the final answer is:
\[ y = -2(x + 3)^2 - 1 \]
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola. From your information, the vertex is given as \((-3, -1)\). This means:
- \(h = -3\)
- \(k = -1\)
You also have the coefficient \(a = -2\).
Putting it all together, the equation in vertex form becomes:
\[ y = -2(x - (-3))^2 + (-1) \]
This simplifies to:
\[ y = -2(x + 3)^2 - 1 \]
So, in the form you provided \(y = -2(x - \_\_)^2 + \_\_\), the blanks are filled in as:
- For the first blank: \(-3\)
- For the second blank: \(-1\)
Thus, the final answer is:
\[ y = -2(x + 3)^2 - 1 \]