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Gianni Greene
Mathematics
31 July, 19:44
Find the vertex form of: y=2x^2-5x+13
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Bautista
31 July, 20:02
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The vertex form of a quadratic function is:
f (x) = a (x - h) ² + k
The coordinate (h, k) represents a parabola's vertex.
In order to convert a quadratic function in standard form to the vertex form, we can complete the square.
y = 2x² - 5x + 13
Move the constant, 13, to the other side of the equation by subtracting it from both sides of the equation.
y - 13 = 2x² - 5x
Factor out 2 on the right side of the equation.
y - 13 = 2 (x² - 2.5x)
Add (b/2) ² to both sides of the equation, but remember that since we factored 2 out on the right side of the equation we have to multiply (b/2) ² by 2 again on the left side.
y - 13 + 2 (2.5/2) ² = 2 (x² - 2.5x + (2.5/2) ²)
y - 13 + 3.125 = 2 (x² - 2.5x + 1.5625)
Add the constants on the left and factor the expression on the right to a perfect square.
y - 9.875 = 2 (x - 1.25) ²
Now, we need y to be by itself again so add 9.875 back to both sides of the equation to move it back to the right side.
y = 2 (x - 1.25) ² + 9.875
Vertex: (1.25, 9.875)
Solution: y = 2 (x - 1.25) ² + 9.875
Or if you prefer fractions
y = 2 (x - 5/4) ² + 79/8
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