Graphing Quadratic Functions

Front

What does it mean if a quadratic function opens down?

Back

The leading coefficient of the quadratic term (ax^2) is negative, indicating that the parabola has a maximum point.

Front

What does it mean if a quadratic function opens up?

Back

The leading coefficient of the quadratic term (ax^2) is positive, indicating that the parabola has a minimum point.

Front

How do you find the vertex of a parabola given in standard form?

Back

Use the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the axis of symmetry in a quadratic function?

Back

The vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What is the vertex of the parabola y = x^2 + 16x + 71?

Back

V(-8, 3) is the vertex.

Front

How can you determine the direction a parabola opens from its equation?

Back

Look at the coefficient of the x^2 term: if it's positive, it opens up; if negative, it opens down.

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax^2 + bx + c.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on its direction.

Front

How do you find the y-intercept of a quadratic function?

Back

Set x = 0 in the equation and solve for y.

Front

What is the formula for the vertex of a parabola in vertex form?

Back

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