#8.3 Graphing ax^2 +bx +c

Front

What is the general form of a quadratic function?

Back

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

Front

What does the coefficient 'a' determine in the quadratic function?

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards (minimum); if 'a' is negative, it opens downwards (maximum).

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you find the x-coordinate of the vertex in a quadratic function?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a).

Front

What is the y-intercept of a quadratic function?

Back

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

Front

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

Back

You can determine if a quadratic function has a maximum or minimum value by looking at the sign of the coefficient 'a': if 'a' is positive, it has a minimum; if 'a' is negative, it has a maximum.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if it's positive, there are two real roots; if it's zero, there is one real root; if it's negative, there are no real roots.

Front

How do you find the y-coordinate of the vertex using the vertex formula?

Back

To find the y-coordinate of the vertex, substitute the x-coordinate found using x = -b/(2a) back into the original quadratic function.

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

What is the standard form of a quadratic function?

Back

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