Quadratic formula

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

Identify the 'a' value in the quadratic equation y = ax² + bx + c.

Back

The 'a' value is the coefficient of x² in the quadratic equation.

Front

Identify the 'b' value in the quadratic equation y = ax² + bx + c.

Back

The 'b' value is the coefficient of x in the quadratic equation.

Front

Identify the 'c' value in the quadratic equation y = ax² + bx + c.

Back

The 'c' value is the constant term in the quadratic equation.

Front

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

Back

The discriminant indicates the nature of the roots of the quadratic equation: if > 0, two distinct real roots; if = 0, one real root; if < 0, no real roots.

Front

For the equation y = 2x² - x - 3, calculate b² - 4ac.

Back

b² - 4ac = (-1)² - 4(2)(-3) = 1 + 24 = 25.

Front

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

Back

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

Front

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

Back

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

Front

What is the axis of symmetry for a quadratic function?

Back

The axis of symmetry is the vertical line x = -b/(2a).

Front

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

Back

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