Front

What is the solution to the system of equations: y=2x+6 and y=x^2+4x+3?

Back

The solution can be found by graphing both equations and identifying their intersection points.

Front

What transformations are applied to the graph of f(x) to obtain g(x) = -\frac{1}{2}f(x-4)+1?

Back

Reflected across x-axis, compressed by 1/2, shifted 4 units right and 1 unit up.

Front

If g(x) = f(x) - 5, how does the graph of g(x) relate to f(x)?

Back

The graph of g(x) is shifted down 5 units from the graph of f(x).

Front

Solve the inequality: 2x^2 + 5x ≥ 12.

Back

The solution is (−∞, -4] U [1.5, ∞).

Front

What transformation does g(x) = f(x + 3) represent?

Back

The graph of g(x) is shifted left 3 units from the graph of f(x).

Front

What is the vertex form of a quadratic function?

Back

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

Front

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

Back

Set f(x) = 0 and solve for x using factoring, completing the square, or the quadratic formula.

Front

What does it mean for a function to be reflected across the x-axis?

Back

The output values of the function are multiplied by -1, changing the sign of all y-values.

Front

What is the effect of compressing a function vertically by a factor of 1/2?

Back

The y-values of the function are halved, making the graph closer to the x-axis.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: two real roots, one real root, or no real roots.