Unit 4 Review

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you find the solutions to a quadratic equation?

Back

You can find the solutions to a quadratic equation using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant of a quadratic equation tell you?

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 two complex roots.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry for a quadratic function in standard form ax^2 + bx + c is 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, the parabola opens upwards; if a < 0, it opens downwards.

Front

How can you determine the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function occurs at the vertex, which can be found using the vertex form or by calculating f(-b/(2a)).

Front

What is the relationship between the roots of a quadratic equation and its graph?

Back

The roots of a quadratic equation correspond to the x-intercepts of its graph, where the function equals zero.

Front

How do you solve a quadratic equation by completing the square?

Back

To solve by completing the square, rearrange the equation to isolate the constant, then add the square of half the coefficient of x to both sides, and solve for x.

Front

What is the process for graphing a quadratic function?

Back

To graph a quadratic function, find the vertex, axis of symmetry, x-intercepts (roots), and y-intercept, then plot these points and draw the parabola.