A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The equation of the parabola in vertex form with vertex at (2, 5) and y-intercept at 17 is y=3(x-2)²+5.
A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in the form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
The equation of a parabola whose vertex is at (2,5) can be written as,
y=a(x-2)²+5
Now, as given the y-intercept is 17, therefore, the equation can be written as,
17=a(0-2)²+5
17-5=a(-2)²
12 = 4a
a = 3
Hence, the equation of the parabola in vertex form with vertex at (2, 5) and y-intercept at 17 is y=3(x-2)²+5.
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