Quadratic Formula

Front

What does the 'a' represent in the quadratic equation ax² + bx + c = 0?

Back

The 'a' represents the coefficient of the x² term, which determines the direction and width of the parabola.

Front

What is the first step in solving a quadratic equation?

Back

The first step is to write the equation in standard form, which is ax² + bx + c = 0.

Front

True or False: The quadratic formula can be used to solve quadratic equations that cannot be factored.

Back

True

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

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

Back

The discriminant indicates the nature of the roots: if it's positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Front

How do you determine if a quadratic equation opens upwards or downwards?

Back

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

Front

What is the vertex of a parabola in the context of a quadratic equation?

Back

The vertex is the highest or lowest point of the parabola, found at the coordinates (h, k) where h = -b/(2a) and k is the value of the quadratic function at h.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What is the significance of the y-intercept in a quadratic equation?

Back

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