Graphs of Parabolas

Front

What is a parabola?

Back

A parabola is a U-shaped curve that is the graph of a quadratic function. It can open upwards or downwards.

Front

What is the vertex of a parabola?

Back

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

Front

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

Back

To find the y-intercept, set x = 0 in the quadratic equation and solve for y.

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. It can be found using the formula x = -b/(2a) for the quadratic equation ax^2 + bx + c.

Front

What does the coefficient of x^2 indicate about a parabola?

Back

The coefficient of x^2 determines the direction of the parabola: if it's positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c.

Front

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

Back

If the coefficient 'a' in the quadratic equation f(x) = ax^2 + bx + c is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the formula for finding the vertex of a parabola 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 significance of the y-intercept in a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis, indicating the value of the function when x = 0.

Front

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

Back

The roots of a quadratic equation are the x-values where the parabola intersects the x-axis.