Key features of parabolas

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts are the points where the parabola crosses the x-axis, found by setting y=0.

Front

What is the axis of symmetry 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 find the vertex of a quadratic equation in vertex form?

Back

For a quadratic equation in the form y = a(x-h)² + k, the vertex is at the point (h, k).

Front

If a parabola opens upwards, what can be said about its vertex?

Back

The vertex is the lowest point of the parabola.

Front

If a parabola opens downwards, what can be said about its vertex?

Back

The vertex is the highest point of the parabola.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c, where a, b, and c are constants.

Front

How do you determine the direction a parabola opens?

Back

If the coefficient 'a' in the quadratic equation is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the significance of the vertex in a parabola?

Back

The vertex represents the maximum or minimum value of the quadratic function.

Front

How can you find the y-intercept of a parabola?

Back

The y-intercept is found by evaluating the quadratic equation at x=0.

Front

What is the formula to find the x-coordinate of the vertex in standard form?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a).