Transformations of Quadratics

Front

What is the parent function of a quadratic?

Back

The parent function of a quadratic is y = x^2.

Front

How do you find the vertex of a quadratic function in vertex form?

Back

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

Front

What is the vertex of the parabola f(x) = -3(x+1)^2 - 7?

Back

The vertex is (-1, -7).

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, but in application-based questions, it may be restricted based on context.

Front

What transformation occurs when f(x) = x^2 is changed to g(x) = (x + 4)^2?

Back

The graph is shifted 4 units to the left.

Front

What is the range of a quadratic function that opens upwards?

Back

The range is [k, ∞) where k is the y-coordinate of the vertex.

Front

What does the 'a' value in the quadratic function f(x) = ax^2 + bx + c determine?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient 'a' in f(x) = ax^2 + bx + c is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the axis of symmetry for a quadratic function?

Back

The axis of symmetry is the vertical line x = -b/(2a) for the quadratic function f(x) = ax^2 + bx + c.

Front

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

Back

You can find the x-intercepts by setting f(x) = 0 and solving the equation ax^2 + bx + c = 0.