Flashcard 4.1-4.3 Solve Quadratics

Front

Solve the quadratic equation: x² + 44 = -15x

Back

The solutions are: {-11, -4}

Front

Which of the following equations matches the standard form of a quadratic? 1. ax + by = c 2. y = a(x - h)² + k 3. y = ax² + bx + c 4. y = mx + b

Back

The correct equation is: y = ax² + bx + c

Front

What is the axis of symmetry for the function f(x) = x² - 8x + 15?

Back

The axis of symmetry is: x = 4

Front

What are the solutions of the graph represented by the quadratic equation? Options: 1. -2 and 3 2. -1/2 and -6 3. -2 and -6 4. 3 and -6

Back

The solutions are: -2 and 3

Front

What is the vertex of the function f(x) = -x² - 4x + 12?

Back

The vertex is: (-2, 16)

Front

Define a quadratic equation.

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic function?

Back

The standard form is: f(x) = ax² + bx + c.

Front

What does the vertex of a parabola represent?

Back

The vertex represents the highest or lowest point of the parabola, depending on its orientation.

Front

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

Back

The axis of symmetry can be found using the formula: x = -b/(2a), where a and b are coefficients from the standard form of the quadratic.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.