Determine whether the parabola opens up, down, right, or left. Find its vertex and axis of symme

step 1 For this equation, we're given x equals 3y squared plus 12 -I minus 7. So the first thing we wan

Determine whether the parabola opens up, down, right, or...

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Key Concepts

Axis of Symmetry

The axis of symmetry is a line that divides the parabola into two symmetric halves. It always passes through the vertex and its orientation (vertical or horizontal) depends on the orientation of the parabola.

Completing the Square

Completing the square is an algebraic technique used to rewrite quadratic equations in their standard or vertex form. This transformation reveals key features of the parabola, such as its vertex and the axis of symmetry, by isolating a perfect square trinomial.

Parabola Orientation

This concept involves determining the direction in which the parabola opens. The orientation of a parabola is determined by which variable is squared. If the equation is of the form x = ay² + by + c, the parabola opens horizontally (either right or left) with the sign of the coefficient 'a' indicating the specific direction: if a > 0, it opens to the right; if a < 0, it opens to the left.

Vertex of a Parabola

The vertex is the point where the parabola changes direction and represents the maximum or minimum point of the curve. In the vertex form of a parabola, this point is clearly identified, and finding the vertex often involves rewriting the equation into this form.

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