Day 1: Introduction to Quadratic Functions

What is the quadratic formula?

• x = (-b ± √(b² - 4ac)) / (2a)

• x = (b ± √(b² + 4ac)) / (2a)

• x = (-b ± √(b² + 4ac)) / (2a)

• x = (b ± √(b² - 4ac)) / (2a)

What shape do quadratic equations take when graphed?

• Circle

• Parabola

• Ellipse

• Hyperbola

What is the equation for the axis of symmetry in a quadratic function?

• x = -b/(2a), where a and b are coefficients from the quadratic equation ax^2 + bx + c = 0.

• x = -b/(a^2 + c), where a and b are coefficients from the quadratic equation ax^2 + bx + c = 0.

• x = -b/(2c), where a and b are coefficients from the quadratic equation ax^2 + bx + c = 0.

• x = -2b/a, where a and b are coefficients from the quadratic equation ax^2 + bx + c = 0.

What is the axis of symmetry in a quadratic function?

• A horizontal line that passes through the vertex, given by the equation y = k.

• A vertical line that passes through the vertex, given by the equation x = h.

• A diagonal line that intersects the x-axis at two points.

• A line that divides the parabola into two equal halves, given by the equation y = mx + b.

What is the maximum or minimum point of a parabola called?

• Vertex

• Focus

• Axis of Symmetry

• Directrix

How can you determine if a parabola opens upwards or downwards?

• If the coefficient of x^2 (a) is positive, it opens upwards.

• If the coefficient of x^2 (a) is negative, it opens upwards.

• If the coefficient of x^2 (a) is zero, it opens downwards.

• If the coefficient of x^2 (a) is positive, it opens downwards.

What is the significance of the vertex in a quadratic function?

• It represents the highest or lowest point of the graph, depending on the direction the parabola opens.

• It is the point where the graph intersects the x-axis.

• It indicates the slope of the parabola at that point.

• It is the midpoint of the parabola's base.

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

• It shifts the graph up or down without affecting the shape or direction of the parabola.

• It changes the width of the parabola.

• It reflects the graph across the x-axis.

• It moves the vertex of the parabola left or right.

What does the discriminant (b² - 4ac) tell you about the roots of a quadratic equation?

• It indicates the nature of the roots: positive means two real roots, zero means one real root, and negative means no real roots.

• It determines the slope of the quadratic function.

• It provides the vertex of the parabola.

• It indicates the maximum value of the quadratic function.

What is the vertex form of a quadratic function?

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

• f(x) = ax² + bx + c, where a, b, and c are constants.

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

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