Algebra 1 EOC Review - Quadratic Functions

What is the end behavior of a quadratic function?

• If a > 0, as x → ±∞, f(x) → +∞; if a < 0, as x → ±∞, f(x) → -∞.

• If a = 0, as x → ±∞, f(x) → 0; if a > 0, as x → ±∞, f(x) → +∞.

• If a < 0, as x → ±∞, f(x) → +∞; if a > 0, as x → ±∞, f(x) → -∞.

• As x → ±∞, f(x) remains constant regardless of the value of a.

How do you factor a quadratic expression?

• Look for two numbers that multiply to give the constant term (c) and add to give the coefficient of the linear term (b).

• Use the quadratic formula to find the roots of the equation.

• Add the coefficients of the quadratic terms together.

• Multiply the linear term by the constant term and then factor the result.

What is an arithmetic sequence?

• A sequence of numbers where each term is multiplied by a constant factor.

• A sequence of numbers in which the difference between consecutive terms is constant.

• A sequence of numbers that follows a geometric pattern.

• A sequence of numbers that is randomly generated.

What is the vertex of a parabola?

• The point where the parabola intersects the x-axis.

• The highest or lowest point on the graph, depending on whether it opens upwards or downwards.

• The point where the parabola intersects the y-axis.

• The midpoint of the line segment connecting the focus and directrix.

What is the axis of symmetry in a quadratic function?

• A vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

• A horizontal line that intersects the vertex of the parabola.

• The point where the parabola touches the x-axis.

• A diagonal line that runs from the vertex to the x-axis.

What are the x-intercepts of a quadratic function?

• The points where the graph intersects the y-axis.

• The points where the graph intersects the x-axis, found by solving the equation f(x) = 0.

• The maximum points of the quadratic function.

• The minimum points of the quadratic function.

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

• By calculating the roots of the equation using the quadratic formula.

• By finding the vertex using the formula k in the vertex form f(x) = a(x-h)² + k.

• By taking the derivative of the function and setting it to zero.

• By evaluating the function at several points and comparing the values.

What is the standard form of a quadratic function?

• f(x) = ax² + bx + c

• f(x) = a(x - h)² + k

• f(x) = a(x + b)(x - c)

• f(x) = ax³ + bx² + cx + d

How do you solve a quadratic equation by factoring?

• Rewrite the equation in the form (x - p)(x - q) = 0, then set each factor to zero and solve for x.

• Use the quadratic formula to find the roots of the equation.

• Graph the equation and find the x-intercepts.

• Complete the square to solve the equation.

What is the discriminant in a quadratic equation?

• The coefficient of the linear term in the equation.

• The part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.

• The constant term in the equation.

• The sum of the roots of the equation.