Unit 5 - Solving Quadratic Equations

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is given by: ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

Identify the 'a' value in the quadratic equation: y = 16x² - 8x - 24.

Back

The 'a' value is 16.

Front

What does the 'b' value represent in a quadratic equation?

Back

The 'b' value represents the coefficient of the linear term in the quadratic equation.

Front

How do you factor the quadratic expression x² - x - 12?

Back

The factors are (x + 3)(x - 4).

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the significance of the 'c' value in a quadratic equation?

Back

The 'c' value is the constant term in the quadratic equation, representing the y-intercept of the graph.

Front

How can you determine the number of real solutions of a quadratic equation using the discriminant?

Back

The discriminant is given by b² - 4ac. If it is positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

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 convert a quadratic equation from standard form to vertex form?

Back

You can convert by completing the square.

Front

What is the axis of symmetry in a quadratic function?

Back

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