Unit 3: Quadratic Functions STUDY GUIDE

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by the equation: y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What does the coefficient 'a' in the quadratic function y = ax² + bx + c determine?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

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

Back

The maximum or minimum value of a quadratic function can be found at the vertex, which occurs at x = -b/(2a). If 'a' is positive, it is a minimum; if 'a' is negative, it is a maximum.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation and is given by: x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert from standard form (y = ax² + bx + c) to vertex form (y = a(x - h)² + k), complete the square.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves and is given by the equation x = -b/(2a).

Front

What is the significance of the roots of a quadratic equation?

Back

The roots of a quadratic equation are the x-values where the graph intersects the x-axis, representing the solutions to the equation.

Front

How do you determine the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0, which gives the value of c in the standard form y = ax² + bx + c.

Front

What is the relationship between the factors of a quadratic equation and its roots?

Back

The roots of a quadratic equation correspond to the values of x that make the equation equal to zero, and can be expressed in factored form as y = a(x - r1)(x - r2), where r1 and r2 are the roots.