Key Features of Quadratics

What is the standard form of a quadratic equation?

• y = ax² + bx + c

• y = ax + b

• y = a + bx + c

• y = ax² + c

What is a quadratic function?

• A polynomial function of degree 1

• A polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

• A linear function that graphs to a straight line

• A function that has no variables and is a constant value.

What is the effect of changing the value of 'c' in a quadratic function?

• It shifts the graph left or right along the x-axis.

• It changes the width of the parabola.

• It shifts the graph up or down along the y-axis without affecting the shape of the parabola.

• It reflects the graph across the x-axis.

What is the vertex form of a quadratic function?

• y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

• y = ax² + bx + c, where a, b, and c are constants.

• y = a(x + h)² + k, where (h, k) is the vertex of the parabola.

• y = a(x - h)² - k, where (h, k) is the vertex of the parabola.

What is the formula for finding the zeros of a quadratic function?

• x = (-b ± √(b² - 4ac)) / (2a)

• x = (b ± √(b² + 4ac)) / (2a)

• x = (-b ± √(b² + 4ac)) / (2a)

• x = (b ± √(b² - 4ac)) / (2a)

How do you find the axis of symmetry for a quadratic function?

• x = -b/(2a)

• x = b/(2a)

• x = -a/(2b)

• x = a/(2b)

What does it mean if the vertex is a maximum?

• The parabola opens upwards, and the vertex is the lowest point on the graph.

• The parabola opens downwards, and the vertex represents the highest point on the graph.

• The vertex is the midpoint of the parabola, regardless of its direction.

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

What are the zeros of a quadratic function?

• The points where the graph reaches its maximum value.

• The x-values where the graph intersects the x-axis, meaning f(x) = 0.

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

• The points where the graph is concave up.

What is the vertex of a quadratic function?

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

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

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

• The midpoint of the line segment connecting the x-intercepts.

How can you determine the number of zeros a quadratic function has?

• By using the vertex form of the quadratic equation.

• By calculating the discriminant (D = b² - 4ac). If D > 0, there are 2 real zeros; D = 0 means 1 real zero; D < 0 means no real zeros.

• By graphing the function and counting the x-intercepts.

• By finding the maximum value of the quadratic function.