Quadratics

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of a parabola, depending on its orientation.

Front

What does the axis of symmetry represent in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, passing through the vertex.

Front

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

Back

If the coefficient of the x^2 term in the quadratic equation is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the minimum value of a parabola that opens upwards?

Back

The minimum value is the y-coordinate of the vertex.

Front

What is the maximum value of a parabola that opens downwards?

Back

The maximum value is the y-coordinate of the vertex.

Front

How can you find the axis of symmetry from the vertex?

Back

The axis of symmetry can be found using the x-coordinate of the vertex, expressed as x = h, where (h,k) is the vertex.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value determines the direction of the parabola (upward or downward) and affects the width of the parabola.

Front

What is the formula to find the vertex of a parabola given in standard form?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h).

Front

What is the relationship between the roots of a quadratic equation and its graph?

Back

The roots of the quadratic equation are the x-intercepts of the graph, where the parabola crosses the x-axis.