Graphs of Parabolas

Front

What is a parabola?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does the coefficient 'a' in a quadratic equation determine?

Back

The coefficient 'a' determines the direction in which the parabola opens: if 'a' is positive, it opens upward; if 'a' is negative, it opens downward.

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 axis of symmetry of a parabola?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the quadratic equation in standard form.

Front

What is the y-intercept of a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis, found by evaluating f(0) in the quadratic equation.

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts, also known as roots, are the points where the parabola crosses the x-axis, found by solving f(x) = 0.

Front

What is the significance of the constant 'c' in a quadratic equation?

Back

The constant 'c' represents the y-intercept of the parabola.

Front

What does it mean for a parabola to open upward?

Back

A parabola opens upward when its vertex is the lowest point, and it extends infinitely in the positive y-direction.

Front

What does it mean for a parabola to open downward?

Back

A parabola opens downward when its vertex is the highest point, and it extends infinitely in the negative y-direction.