#8.1 Graphing f(x) = ax^2

Front

What is the equation for the axis of symmetry in a quadratic function?

Back

x = -b/(2a), where a and b are coefficients from the quadratic equation f(x) = ax^2 + bx + c.

Front

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

Back

y ≥ k, where (h, k) is the vertex of the parabola.

Front

When is a quadratic function decreasing?

Back

A quadratic function is decreasing on the interval (-∞, h) where (h, k) is the vertex.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, given by the coordinates (h, k) in the vertex form f(x) = a(x-h)^2 + k.

Front

What is the domain of a quadratic function?

Back

All real numbers, represented as (-∞, ∞).

Front

How do you find the y-intercept of a quadratic function?

Back

Set x = 0 in the equation f(x) = ax^2 + bx + c and solve for f(0) = c.

Front

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

Back

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

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b^2 - 4ac) determines the nature of the roots: D > 0 means two real roots, D = 0 means one real root, D < 0 means no real roots.

Front

How do you determine if a quadratic function is increasing?

Back

A quadratic function is increasing on the interval (h, ∞) where (h, k) is the vertex.

Front

What is the standard form of a quadratic function?

Back

f(x) = ax^2 + bx + c.