Graphing Quadratics-3 methods

Front

What are the three methods for graphing quadratic functions?

Back

1. Factoring 2. Completing the square 3. Using the quadratic formula

Front

What is the general form of a quadratic function?

Back

y = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the vertex of a parabola represent in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola.

Front

How can you determine if a quadratic function has a maximum or minimum?

Back

If the coefficient 'a' is positive, the parabola opens upwards and has a minimum. If 'a' is negative, it opens downwards and has a maximum.

Front

What is the vertex form of a quadratic function?

Back

y = a(x - h)^2 + k, where (h, k) is the vertex.

Front

How do you find the x-intercepts of a quadratic function?

Back

Set y = 0 and solve the equation ax^2 + bx + c = 0.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line that passes through the vertex, given by x = -b/(2a).

Front

What does the discriminant of a quadratic equation tell you?

Back

The discriminant (D = b^2 - 4ac) indicates the nature of the roots: D > 0 means two real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

How can you convert a quadratic function from standard form to vertex form?

Back

Use the method of completing the square.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.