Properties of parabolas and graphing parabolas

Front

What is the standard form of a quadratic equation?

Back

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

Front

How do you find the axis of symmetry of a parabola given the equation y = ax² + bx + c?

Back

The axis of symmetry can be found using the formula x = -b/2a.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the significance of the coefficient 'a' in the quadratic equation y = ax² + bx + c?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

How can you find the y-coordinate of the vertex of a parabola?

Back

To find the y-coordinate of the vertex, substitute the x-coordinate of the vertex (x = -b/2a) back into the equation y = ax² + bx + c.

Front

What is the y-intercept of a quadratic equation?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the equation at x = 0.

Front

If a quadratic equation is in the form y = ax² + bx + c, what are A, B, and C?

Back

A is the coefficient of x², B is the coefficient of x, and C is the constant term.

Front

What is the formula to find the x-intercepts of a parabola?

Back

The x-intercepts can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant (b² - 4ac) tell us about the roots of a quadratic equation?

Back

The discriminant indicates the nature of the roots: if > 0, there are two real roots; if = 0, there is one real root; if < 0, there are no real roots.

Front

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

Back

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