Quadratics review

Front

What are the solutions, roots, x-intercepts, and zeros of a quadratic equation?

Back

They are all the same thing, referring to the values of x where the quadratic equation equals zero.

Front

How can you determine if a quadratic equation opens up or down?

Back

If the coefficient of the x^2 term is positive, the parabola opens up; if it is negative, it opens down.

Front

What is another term for the zeros of a quadratic function?

Back

Roots.

Front

What are x-intercepts in the context of a quadratic function?

Back

They are the points where the graph of the function intersects the x-axis, corresponding to the roots of the equation.

Front

How do you factor the quadratic expression (x+3)(x-2)?

Back

Set each factor equal to zero: x+3=0 gives x=-3, and x-2=0 gives x=2.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

What does the vertex of a parabola represent?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens up or down.

Front

How can you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, then substituting back to find the y-coordinate.

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 you?

Back

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