Finding the Vertex of a Parabola

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the point where the parabola changes direction. It is the highest or lowest point of the graph, depending on whether the parabola opens upwards or downwards.

Front

How do you find the vertex of a parabola given in standard form y = ax^2 + bx + c?

Back

The vertex can be found using the formula: x = -b/(2a). Once you find x, substitute it back into the equation to find the y-coordinate.

Front

Find the vertex of the parabola given by the equation y = 2x^2 - 8x + 5.

Back

The vertex is at (2, -3).

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum value of the quadratic function, which is important for understanding the function's behavior.

Front

How does the value of 'a' in the equation y = ax^2 + bx + c affect the vertex?

Back

The value of 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

Find the vertex of the parabola y = -3x^2 + 6x - 1.

Back

The vertex is at (1, 2).

Front

What is the formula for the vertex of a parabola in vertex form y = a(x-h)^2 + k?

Back

The vertex is at the point (h, k).

Front

Find the vertex of the parabola given by the equation y = x^2 + 4x + 4.

Back

The vertex is at (-2, 0).

Front

What does it mean if the vertex of a parabola is at a negative y-coordinate?

Back

It means that the highest or lowest point of the parabola is below the x-axis, indicating that the function has negative values at its vertex.

Front

How can you determine if a parabola opens upwards or downwards?

Back

If the coefficient 'a' in the equation y = ax^2 + bx + c is positive, the parabola opens upwards. If 'a' is negative, it opens downwards.