Question

Suppose the function shown below was expressed in standard form, y=ax^2+bx+c. What is the value of a? the graph shows a parabola facing downward with a vertex of (1,4) and the x intercepts are (3,0) and (-1,0) with a y intercept of (0,3)

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Answer 1

This is the graph they are referring to

Answer 2

y = -a(x - 1)^2 + 4 = -a(x^2 - 2x + 1) + 4 = -ax^2 + 2ax - a + 4 . . . (1)
y = -a(x - 3)(x + 1) = -a(x^2 - 2x - 3) = -ax^2 + 2ax + 3a . . . (2)

Equating (1) and (2), we have that
-a + 4 = 3a
3a + a = 4
4a = 4
a = 1

Required equation is
y = -x^2 + 2x + 3

Therefore, a = -1