Kotik Intro to Quadratic

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the formula to find the vertex of a quadratic function in standard form?

Back

The vertex (h, k) of a quadratic function f(x) = ax^2 + bx + c can be found using h = -b/(2a) and k = f(h).

Front

What does the line of symmetry of a quadratic function represent?

Back

The line of symmetry of a quadratic function is a vertical line that divides the parabola into two mirror-image halves. It passes through the vertex.

Front

How do you find the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function can be found by setting f(x) = 0 and solving the equation ax^2 + bx + c = 0.

Front

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

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 concavity of a quadratic function?

Back

The concavity of a quadratic function is determined by the sign of the coefficient 'a': if a > 0, the function is concave up; if a < 0, it is concave down.

Front

How can you determine the vertex of a quadratic function from its graph?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards.

Front

What is the quadratic formula used for?

Back

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

Front

What is the discriminant in a quadratic equation, and what does it indicate?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac. It indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What are the coordinates of the vertex for the function f(x) = x^2 - 4x + 3?

Back

The vertex of the function f(x) = x^2 - 4x + 3 is (2, -1).