A.O.S. & Vertex of Quadratics 11/4/24

Front

What is the vertex of a quadratic function?

Back

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

Front

What does the axis of symmetry represent in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves.

Front

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

Back

If the coefficient of the x^2 term is positive, the parabola opens upwards and has a minimum value. If it is negative, the parabola opens downwards and has a maximum value.

Front

What is the standard form of a quadratic function?

Back

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

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula V(-b/2a, f(-b/2a)).

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the vertex of the quadratic function y = x^2 - 4x + 3?

Back

V(2, -1) is the vertex.

Front

What is the axis of symmetry for the quadratic function y = 2x^2 + 8x + 6?

Back

The axis of symmetry is x = -2.

Front

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

Back

Use the method of completing the square to rewrite the function in the form y = a(x-h)^2 + k.

Front

What is the vertex form of a quadratic function?

Back

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