Quadratic Formula

Front

What is the quadratic formula?

Back

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

Front

What are the standard form coefficients in a quadratic equation?

Back

In the standard form of a quadratic equation ax² + bx + c = 0, a, b, and c are the coefficients where a is the coefficient of x², b is the coefficient of x, and c is the constant term.

Front

How do you identify a, b, and c in the equation x² - 6x + 14?

Back

In the equation x² - 6x + 14, a = 1, b = -6, and c = 14.

Front

What is the first step in solving a quadratic equation using the quadratic formula?

Back

The first step is to rearrange the equation into standard form (ax² + bx + c = 0) if it is not already in that form.

Front

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

Back

The discriminant indicates the nature of the roots: if it is positive, there are two distinct real roots; if it is zero, there is one real root (a repeated root); if it is negative, there are no real roots (the roots are complex).

Front

How do you solve the equation x² + 4x - 40 = -8 using the quadratic formula?

Back

First, rearrange to x² + 4x + 32 = 0. Then identify a = 1, b = 4, c = 32, and apply the quadratic formula to find the roots.

Front

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

Back

The 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 vertex of a parabola represented by a quadratic equation?

Back

The vertex of a parabola given by the equation y = ax² + bx + c 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 a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

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

Back

To convert from standard form (y = ax² + bx + c) to vertex form (y = a(x-h)² + k), complete the square.