Ch 10 Part 2 Quadratic Equations/Inequalities

Front

What is a quadratic equation?

Back

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

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

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 the direction it opens.

Front

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the quadratic equation ax² + bx + c.

Front

What is the significance of the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph crosses the x-axis, representing the solutions to the equation when y = 0.

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 tell us about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if > 0, two real solutions; if = 0, one real solution; if < 0, no real solutions.

Front

What is a zero of a function?

Back

A zero of a function is a value of x that makes the function equal to zero.

Front

How can you determine the number of solutions from a graph of a quadratic function?

Back

The number of solutions corresponds to the number of times the graph intersects the x-axis.