Unit 3 Review - Lessons 7 - 11

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you complete the square for the expression x² + 16x?

Back

To complete the square, take half of the coefficient of x (which is 16), square it (8² = 64), and add it to the expression: x² + 16x + 64 = (x + 8)².

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

Back

Front

What is the process to solve a quadratic equation using square roots?

Back

To solve a quadratic equation of the form a(x - p)² = q, isolate (x - p)², take the square root of both sides, and solve for x.

Front

What is the value that completes the square for x² + 16x?

Back

The value that completes the square is 64.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

How do you find the vertex of a parabola given in standard form?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h).

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

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

Front

What is the formula for the quadratic formula?

Back