Quadratics Review

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you find the roots of a quadratic equation?

Back

To find the roots of a quadratic equation, you can use the quadratic formula: x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

Front

What does the discriminant of a quadratic equation tell you?

Back

The discriminant (D = b^2 - 4ac) indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

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

Back

The vertex of a parabola is the highest or lowest point of the graph, depending on the direction it opens. It can be found using the formula (-b/2a, f(-b/2a)).

Front

How do you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry for a quadratic function in standard form is given by the line x = -b/(2a).

Front

What is the significance of the leading coefficient in a quadratic function?

Back

The leading coefficient (a) determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, as there are no restrictions on the input values.

Front

What is the range of a quadratic function that opens downwards?

Back

The range of a downward-opening quadratic function is y ≤ k, where k is the y-coordinate of the vertex.

Front

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

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form ax^2 + bx + c.

Front

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

Back

The sum of the roots (r1 + r2) is equal to -b/a, and the product of the roots (r1 * r2) is equal to c/a.