Final Exam Review 2: Units 2 & 3 Review

Front

What is the axis of symmetry for the quadratic equation y = 3x^2 - 6x + 4?

Back

The axis of symmetry is x = 1.

Front

How do you model the area of a garden with a uniform path around it?

Back

The equation is (50 + 2x)(70 + 2x) = 4524, where x is the width of the path.

Front

What is the formula for the area of a rectangle?

Back

Area = length × width.

Front

What does the discriminant of a quadratic equation tell you?

Back

The discriminant indicates the nature of the roots: positive means 2 real rational roots, zero means 1 real root, and negative means 2 imaginary roots.

Front

What is the formula for the discriminant of a quadratic equation ax^2 + bx + c?

Back

The discriminant is given by D = b^2 - 4ac.

Front

How do you find the vertex of a parabola given by the equation y = ax^2 + bx + c?

Back

The vertex can be found at x = -b/(2a).

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax^2 + bx + c.

Front

What is the significance of the leading coefficient in a quadratic equation?

Back

The leading coefficient (a) determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

How do you calculate the area of a shaded region between two curves?

Back

Integrate the top function minus the bottom function over the interval of interest.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 × base × height.