Question
In vertex form, write the equation for the quadratic function shown on the graph.
(1 point)
y=3
(x−
)2+
A coordinate plane's x-axis ranges from negative 4 to 4 and its y-axis ranges from negative 1 to 6, both by 1-unit increments. A concave up parabola is drawn in the first quadrant.
(1 point)
y=3
(x−
)2+
A coordinate plane's x-axis ranges from negative 4 to 4 and its y-axis ranges from negative 1 to 6, both by 1-unit increments. A concave up parabola is drawn in the first quadrant.
Answers
GPT-4o mini
To write the equation of a quadratic function in vertex form, we use the format:
\[
y = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex of the parabola, and \(a\) determines the width and direction of the opening.
From the description, the parabola is concave up and located in the first quadrant. This suggests that the vertex is probably at a point where both \(h\) and \(k\) are positive.
Without seeing the graph, I can help guide you in filling in the values.
1. **Find the vertex \((h, k)\)**: Look at the graph to identify the coordinates of the vertex.
- The x-coordinate of the vertex, \(h\), is where the parabola reaches its minimum.
- The y-coordinate of the vertex, \(k\), is the corresponding value.
2. **Identify the value of \(a\)**:
- Check how wide the parabola is. If it opens wide, \(a\) is a small positive number. If it is narrow, \(a\) is a larger positive number.
Assuming you are able to identify these, you can substitute \(h\), \(k\), and \(a\) into the vertex form equation.
For example, if the vertex were at \((2, 3)\) and \(a = 1\), the equation would be:
\[
y = 1(x - 2)^2 + 3
\]
If you provide more specifics about the vertex and the width of the parabola or if more information about the graph is available, I can help refine it further!
\[
y = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex of the parabola, and \(a\) determines the width and direction of the opening.
From the description, the parabola is concave up and located in the first quadrant. This suggests that the vertex is probably at a point where both \(h\) and \(k\) are positive.
Without seeing the graph, I can help guide you in filling in the values.
1. **Find the vertex \((h, k)\)**: Look at the graph to identify the coordinates of the vertex.
- The x-coordinate of the vertex, \(h\), is where the parabola reaches its minimum.
- The y-coordinate of the vertex, \(k\), is the corresponding value.
2. **Identify the value of \(a\)**:
- Check how wide the parabola is. If it opens wide, \(a\) is a small positive number. If it is narrow, \(a\) is a larger positive number.
Assuming you are able to identify these, you can substitute \(h\), \(k\), and \(a\) into the vertex form equation.
For example, if the vertex were at \((2, 3)\) and \(a = 1\), the equation would be:
\[
y = 1(x - 2)^2 + 3
\]
If you provide more specifics about the vertex and the width of the parabola or if more information about the graph is available, I can help refine it further!