Quadratic Solutions & Transformations

Front

What are the solutions of the quadratic equation represented by the graph?

Back

The solutions are the x-intercepts of the graph.

Front

What does it mean when a quadratic function is reflected over the x-axis?

Back

It means that the graph of the function is flipped upside down.

Front

What is the result of completing the square for the function: f(x) = x² + 12x - 2?

Back

f(x) = (x + 6)² - 38.

Front

Solve the equation: x² - 6x + 8 = 0.

Back

The solutions are x = 2 and x = 4.

Front

Solve: x² - 49 = 0.

Back

The solutions are x = -7 and x = 7.

Front

What is the vertex form of a quadratic function?

Back

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

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) from the standard form ax² + bx + c.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: two real and distinct, one real and repeated, or no real roots.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

What transformation occurs when a quadratic function is shifted up by 4 units?

Back

The new function is f(x) = x² + 4.