To find the equation of the quadratic function in the form \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola, we can start with the vertex and then find the value of \(a\) using the second point that the function goes through.
Given:
- Vertex \((h, k) = (7, -3)\)
- Point \((9, 9)\)
Now we can plug in these values into the equation:
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Substituting the vertex into the equation, we have: \[ f(x) = a(x - 7)^2 - 3 \]
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Now, we use the point \((9, 9)\) to find \(a\): \[ f(9) = 9 \implies 9 = a(9 - 7)^2 - 3 \]
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Simplifying this equation: \[ 9 = a(2)^2 - 3 \] \[ 9 = 4a - 3 \] \[ 9 + 3 = 4a \implies 12 = 4a \implies a = 3 \]
Now we can write the final equation:
\[ f(x) = 3(x - 7)^2 - 3 \]
Thus, filling in the boxes:
- The first box: 3
- The second box: 7
- The third box: -3
So the answers are:
\[ f(x) = 3(x - 7)^2 - 3 \]
Finally, the filled boxes will be:
- 3
- 7
- -3
1 answer