Quadratic Formula Practice

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant tell us?

Back

The discriminant (b² - 4ac) determines the nature of the roots of a quadratic equation: if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

Identify the coefficients in the quadratic equation y = 2x² + 3x + 5.

Back

a = 2, b = 3, c = 5.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

Front

Solve the quadratic equation: x² - 4x - 5 = 0.

Back

The solutions are x = 5 and x = -1.

Front

What is the vertex of a parabola represented by the equation y = ax² + bx + c?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert to vertex form, complete the square: y = a(x - h)² + k, where (h, k) is the vertex.

Front

What is the significance of the 'a' coefficient in a quadratic equation?

Back

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

Front

What are the roots of a quadratic equation?

Back

The roots (or solutions) are the values of x that make the equation equal to zero.