Question
In vertex form, write the equation for the quadratic function shown in the graph
The axis of symmetry is at 1, 3. y = 3(x-_)^2+_
The axis of symmetry is at 1, 3. y = 3(x-_)^2+_
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 \(a\) is a coefficient that determines the width and direction of the opening of the parabola.
From your question, it seems like the axis of symmetry is at \(x = 1\), which indicates that the \(h\) value in the vertex form is \(1\). The \(k\) value (the y-coordinate of the vertex) is not given in your statement, so we will need that to complete the equation.
If the vertex of the parabola is at (1, 3), then:
- \(h = 1\)
- \(k = 3\)
Thus, the vertex form will be:
\[ y = a(x - 1)^2 + 3 \]
Now, you need the value of \(a\) to finalize the equation. The value of \(a\) determines if the parabola opens upward (if \(a > 0\)) or downward (if \(a < 0\)), and it affects the width of the parabola. You can find \(a\) by using another point on the graph.
If you can provide a specific point on the graph (other than the vertex), we can solve for \(a\) and complete the equation. Otherwise, the general form with the vertex at (1, 3) is:
\[ y = a(x - 1)^2 + 3 \]
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola and \(a\) is a coefficient that determines the width and direction of the opening of the parabola.
From your question, it seems like the axis of symmetry is at \(x = 1\), which indicates that the \(h\) value in the vertex form is \(1\). The \(k\) value (the y-coordinate of the vertex) is not given in your statement, so we will need that to complete the equation.
If the vertex of the parabola is at (1, 3), then:
- \(h = 1\)
- \(k = 3\)
Thus, the vertex form will be:
\[ y = a(x - 1)^2 + 3 \]
Now, you need the value of \(a\) to finalize the equation. The value of \(a\) determines if the parabola opens upward (if \(a > 0\)) or downward (if \(a < 0\)), and it affects the width of the parabola. You can find \(a\) by using another point on the graph.
If you can provide a specific point on the graph (other than the vertex), we can solve for \(a\) and complete the equation. Otherwise, the general form with the vertex at (1, 3) is:
\[ y = a(x - 1)^2 + 3 \]