Quadratics review

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of a parabola, depending on its orientation. It represents the maximum or minimum value of the quadratic function.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

Front

What does the 'a' value in a quadratic equation determine?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

What are the roots of a quadratic equation?

Back

The roots are the values of x that make the quadratic equation equal to zero. They are also known as the x-intercepts.

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 standard form of the quadratic equation.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, found by evaluating the function at x = 0.

Front

What is the Zero-Product Property?

Back

The Zero-Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How can you determine if a quadratic function has a maximum or minimum value?

Back

You can determine this by looking at the 'a' value in the quadratic equation: if a > 0, it has a minimum; if a < 0, it has a maximum.

Front

What is the significance of the discriminant in a quadratic equation?

Back

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

Front

What is the formula for the vertex of a parabola in standard form?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h).