Answer:
- f(x) = - 1/4x² - 3/2x + 3/4
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We need to find the equation of the parabola in standard form
Observations
- Graph opens down, hence the leading coefficient is negative,
- Vertex is (-3, 3),
- Graph is horizontally stretched, hence the leading coefficient is between - 1 and 0,
- Values of y at x = (vertex - 1) are - 5 and - 1, distance is 4, twice the one without stretch, so the scale factor is 1/2.
Build the equation based on observations
Use the vertex form f(x) = a(x - h)² + k, where (h, k) is vertex and a- constant
- f(x) = - (1/2)² (x + 3) + 3
Convert this to standard form
- f(x) =
- - 1/4(x² + 6x + 9) + 3 =
- - 1/4x² - 6/4x - 9/4 + 3 =
- - 1/4x² - 3/2x + 3/4