Week 2 Graphing Features & Solving Quadratics Word Problems

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a' in the equation.

Front

What is the vertex of a parabola?

Back

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

Front

How do you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value can be found at the vertex of the parabola, which occurs at t = -b/(2a) for the quadratic equation ax² + bx + c.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero; they are the x-intercepts of the graph.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How do you solve a word problem involving area and dimensions?

Back

Set up an equation based on the area formula (Area = length × width) and any relationships between dimensions, then solve for the unknowns.

Front

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

Back

The coefficient 'a' determines the direction and width of the parabola, 'b' affects the position of the vertex, and 'c' represents the y-intercept.

Front

How can you determine the width and length of a rectangle from its area?

Back

Use the area formula (Area = length × width) and any given relationships between length and width to form equations and solve for the dimensions.