Question
Write the vertex form of a parabola that satisfies the conditions given. Then write the equation in the form y = ax^2 + bx + c
Write the vertex form of a parabola that satisfies the conditions given. Then write the equation in the form
y = ax^2 + bx + c
Vertex (1, 5) and a = -2/3
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Koala Tutor
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Got a question with my answer?
The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
Given the vertex (1, 5) and a = -2/3, we can substitute these values into the vertex form to get:
y = -2/3(x - 1)^2 + 5
To convert this into the form y = ax^2 + bx + c, we first expand the square:
y = -2/3(x^2 - 2x + 1) + 5
Then distribute the -2/3:
y = -2/3x^2 + 4/3x - 2/3 + 5
Finally, simplify the constant term:
y = -2/3x^2 + 4/3x + 13/3
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