The equation of a parabola in standard form can be either of the form \(y = ax^2 + bx + c\) (up/down) or of the form \(x = ay^2 + by + c\) (left/right).
And we have the up/down standard form form, i.e., \(y = x^2 - 6x + 14\) (I'm assuming + sign of 14)
Compare the equation of the parabola with the standard form \(y = ax^2 + bx + c\) , after comparing, we get, a = 1, b = -6 & c = 14
Find the x-coordinate of the vertex using the formula, \(h = \frac{-b}{2a}\)
then, we get h = -(-6)/21 = 6/2 = 3
to find the y-coordinate (k) of the vertex, substitute x = h in the expression \(ax^2+ bx + c\)
then k = 13^2 + (-6)3 + 14 = 9 - 18 + 14 = 5
The vertex (h, k) = (3, 5) as an ordered pair
Therefore, the vertex form of the equation is
\(y = (x - 3)^2 + 5\)
What is the vertex form of quadratic equation?
The vertex form of a quadratic function is \(f(x) = a(x - h)^2 + k\), where a, h, and k are constants of the parabola is at (h, k). When the quadratic parent function \(f(x) = x^2\) is written in vertex form, \(y = a(x - h)^2 + k\), a = 1, h = 0, and k = 0.
What are the 3 form of equation of parabola
Left/Right Opened Parabolas:
Standard form: \(x = ay^2 + by + c\)
Vertex Form: \(x = a (y - k)^2 + h\)
Intercept Form: \(x = a(y - p)(y - q)\)
Top/Bottom Opened Parabolas:
Standard form: \(y = ax^2 + bx + c\)
Vertex Form: \(y = a (x - h)^2 + k\)
Intercept Form: \(y = a(x - p)(x - q)\)
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