Graphing Quadratics

Front

What is a parabola?

Back

A parabola is a symmetrical, U-shaped curve that represents the graph of a quadratic function.

Front

How does the direction of a parabola change with the value of 'a' in the equation y = ax² + bx + c?

Back

If 'a' is positive, the parabola opens upwards. If 'a' is negative, it opens downwards.

Front

What is the vertex of a parabola?

Back

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

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.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0.

Front

What are the roots or x-intercepts of a quadratic function?

Back

The roots or x-intercepts are the points where the parabola crosses the x-axis.

Front

What does it mean if a quadratic equation has no real roots?

Back

It means the parabola does not intersect the x-axis, indicating that the discriminant is less than zero.

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the vertex form of a quadratic function?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How can you determine the direction a parabola opens from its equation?

Back

By looking at the coefficient 'a': if 'a' > 0, it opens up; if 'a' < 0, it opens down.