Quadratics Review

Front

What is a quadratic equation?

Back

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

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 for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts (or zeros) are the points where the graph intersects the x-axis, found by solving the equation ax^2 + bx + c = 0.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions 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 it's positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Front

What is a parabola's focus?

Back

The focus of a parabola is a point from which distances to points on the parabola are measured, and it lies along the axis of symmetry.

Front

What is the difference between the vertex form and standard form of a quadratic function?

Back

The vertex form is f(x) = a(x-h)² + k, where (h, k) is the vertex, while the standard form is f(x) = ax² + bx + c.