Review Quadratics 4B

Front

What is the average rate of change of a function f(x) from x=a to x=b?

Back

The average rate of change of a function f(x) from x=a to x=b is given by the formula: \( \frac{f(b) - f(a)}{b - a} \).

Front

What is the vertex of a quadratic function in the form y=a(x-h)^2+k?

Back

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

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, also known as the zeros of the function.

Front

How do you find the average rate of change of f(x)=2x^2+3x-1 from x=1 to x=2?

Back

To find the average rate of change, calculate: \( \frac{f(2) - f(1)}{2 - 1} \). For this function, it equals 9.

Front

What transformation occurs when a graph is reflected over the x-axis?

Back

When a graph is reflected over the x-axis, the y-coordinates of all points on the graph are multiplied by -1.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is: \( ax^2 + bx + c = 0 \), where a, b, and c are constants.

Front

What does the 'a' value in the quadratic equation y=ax^2+bx+c determine?

Back

The 'a' value determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the axis of symmetry for the quadratic function y=ax^2+bx+c?

Back

The axis of symmetry for the quadratic function is given by the formula: \( x = -\frac{b}{2a} \).

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 > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

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

Back

To convert from vertex form \( y=a(x-h)^2+k \) to standard form, expand the equation and simplify to the form \( ax^2 + bx + c \).