Quadratics flashcard

Front

What is the general form of a quadratic equation?

Back

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

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, there are 2 real solutions; if = 0, there is 1 real solution; if < 0, there are no real solutions (imaginary solutions).

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, located at the point (h, k) in the vertex form y = a(x - h)² + k.

Front

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

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation.

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, the parabola opens upwards; if a < 0, it opens downwards.

Front

What is the quadratic formula used for?

Back

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

Front

What does it mean if a quadratic equation has no real solutions?

Back

It means that the graph of the quadratic does not intersect the x-axis, indicating that the discriminant is less than zero.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex.

Front

How can you determine the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex, which can be found using the vertex form or the axis of symmetry.