To write the equation of a concave up parabola in vertex form, which is \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola, we need to identify the vertex from the description.
Since the parabola is in the first quadrant and concave up, we will identify the vertex point \( (h, k) \).
From the information provided:
- The x-axis ranges from -4 to 4.
- The y-axis ranges from -1 to 6.
- The vertex should be a point located within the first quadrant.
Assuming that the vertex is visible in the range described, we need specific values of \( h \) and \( k \) to fill in the equation.
Without an actual graphical image to refer to, let’s assume the vertex is at \( (h, k) = (1, 2) \) as a hypothetical example.
The value \( a \) indicates the stretching of the parabola. Let's say that the value determined from the graph for \( a \) is 3.
Thus, if:
- \( h = 1 \)
- \( k = 2 \)
- \( a = 3 \)
The vertex form of the quadratic function would then be: \[ y = 3(x - 1)^2 + 2 \]
So, if you need it in a specific answer format:
- Replace \( _ \) with \( 1 \) for \( h \)
- Replace the second \( _ \) with \( 2 \) for \( k \)
Thus, the final equation in vertex form is: \[ y = 3(x - 1)^2 + 2 \]
Fill in the blanks: y = 3(x−1)² + 2
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