Algebra 2 4.5-4.8 Review

Front

What is the process to solve the equation (x - 7)² + 4 = 40?

Back

1. Subtract 4 from both sides: (x - 7)² = 36. 2. Take the square root of both sides: x - 7 = ±6. 3. Solve for x: x = 1 or x = 13.

Front

How do you solve the equation 5(x - 3)² + 1 = 81?

Back

1. Subtract 1 from both sides: 5(x - 3)² = 80. 2. Divide by 5: (x - 3)² = 16. 3. Take the square root: x - 3 = ±4. 4. Solve for x: x = -1 or x = 7.

Front

What is the definition of a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the steps to factor a quadratic expression?

Back

1. Write the expression in standard form. 2. Identify a, b, and c. 3. Find two numbers that multiply to ac and add to b. 4. Rewrite the middle term using these numbers. 5. Factor by grouping.

Front

What is the vertex form of a quadratic function?

Back

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

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does the discriminant of a quadratic equation tell us?

Back

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

Front

How do you complete the square for the equation x² + 6x + 5 = 0?

Back

1. Move the constant to the other side: x² + 6x = -5. 2. Take half of b (3), square it (9), and add to both sides: x² + 6x + 9 = 4. 3. Factor: (x + 3)² = 4. 4. Solve for x.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror images, given by the formula x = -b/(2a).

Front

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

Back

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