Graphing Quadratic Functions

Front

What indicates that a parabola has a minimum?

Back

When ‘a’ is positive in the quadratic equation, the parabola opens upwards and has a minimum point.

Front

How can you determine if a parabola opens up or down?

Back

If the coefficient 'a' in the quadratic equation y = ax^2 + bx + c is positive, the parabola opens up. If 'a' is negative, it opens down.

Front

What is the y-intercept of the function f(x) = 2x^2 - 2x + 1?

Back

The y-intercept is (0, 1). This is found by evaluating f(0).

Front

How do you find the zeros of a parabola?

Back

The zeros of a parabola are the x-values where the function equals zero. They can be found by factoring, using the quadratic formula, or graphing.

Front

What is the formula for finding the axis of symmetry in standard form?

Back

The axis of symmetry for a quadratic in standard form y = ax^2 + bx + c is given by x = -b/(2a).

Front

What does the vertex of a parabola represent?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens up or down.

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, you can complete the square.

Front

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

Back

The 'a' value determines the direction of the parabola (upward or downward) and the width of the parabola.