Question

graph the parabola x=6y^2+24y+25.

Answer 1

The equation is .

The above equation represent the parabola.

Here y ² coefficient is 6, for perfect square make y ² coefficient 1 by factor out 6.

To change the expression into a perfect square trinomial add (half the y coefficient)² to each side of the expression.

Here y coefficient = 4. so, (half the x coefficient)² = (4/2)²= 4.

Add 4 to each side of the equation.

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Compare the equation with The standard form of the parabola with vertex (h, k ) and axis of symmetry y = k  is x = a (y - k)² + h.

Vertex (h, k ) = (1, - 2), and axis of symmetry k  = 1.

Make the table of values to find ordered pairs that satisfy the equation.

Choose values for y and find the corresponding values for x.

y		(x, y)
1		(55,1)
-1		(7,-1)
-2		(1,-2)
-3		(7,-3)
-4		(25,-4)

1.Draw a coordinate plane.

2.Plot the coordinate points.

3.Then sketch the graph, connecting the points with a smooth curve.

The points (55, 1), (7, - 1), (1, - 2), (7, - 3), and (25, - 4) are also on the parabola.

The graph is shifted right 1 unit from the origin (0, 0), and the vertex is (1, - 2).