Construct a quadratic function that has a vertex at (-2,3) and includes the value f(-1)=1.
Answer:
f(x) = -2(x + 2)²+ 3
Step-by-step explanation:
Let the quadratic function be,
f(x) = a(x - h)² + k
Here, (h, k) is the vertex of the parabola
If (-2, 3) is the vertex of the parabola,
f(x) = a(x + 2)² + 3
And f(-1) = 1,
f(-1) = a(-1 + 2)² + 3
1 = a(1) + 3
a = 1 - 3
a = -2
Therefore, quadratic function is,
f(x) = -2(x + 2)²+ 3
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