Understanding the Formula for a Horizontal Parabola and Its Impact on the Direction and Vertex Coordination

Horizontal Parabola Formula

The formula for a horizontal parabola can be written as:

y = a(x – h)^2 + k

where:
– y represents the dependent variable or the output of the equation
– x represents the independent variable or the input to the equation
– (h, k) represents the coordinates of the vertex of the parabola
– a represents the coefficient that determines the width, direction, and steepness of the parabola

In a horizontal parabola, the vertex is shifted horizontally to the right or left

The formula for a horizontal parabola can be written as:

y = a(x – h)^2 + k

where:
– y represents the dependent variable or the output of the equation
– x represents the independent variable or the input to the equation
– (h, k) represents the coordinates of the vertex of the parabola
– a represents the coefficient that determines the width, direction, and steepness of the parabola

In a horizontal parabola, the vertex is shifted horizontally to the right or left. The standard form of the equation helps determine the direction of the shift.

If the equation is in the form y = a(x – h)^2 + k, and a is positive, the parabola opens to the right, and the vertex is shifted h units to the right. If a is negative, the parabola opens to the left, and the vertex is shifted h units to the left.

It’s important to note that the value of a determines the width and steepness of the parabola. A larger absolute value of a results in a narrower and steeper parabola, while a smaller absolute value of a results in a wider and flatter parabola.

In summary, the horizontal parabola formula y = a(x – h)^2 + k represents a parabola that is shifted horizontally by h units, opens to the right or left based on the sign of a, and has its vertex at the coordinates (h, k).

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