Exploring Quadratic Functions

What is the standard form of a quadratic function?

• f(x) = ax^2 + bx + c

• f(x) = a + b + c

• f(x) = ax^3 + bx + c

• f(x) = ax^2 + b

How do you find the vertex of a quadratic function?

• The vertex is found by using the quadratic formula

• The vertex is at (b, 0)

• The vertex is at ( -b/(2a), f(-b/(2a)) )

• The vertex is at (0, 0)

What is the quadratic formula used for?

• To find the roots of a quadratic equation.

• To solve linear equations.

• To calculate the area of a triangle.

• To determine the slope of a line.

Explain the significance of the discriminant in a quadratic equation.

• The discriminant indicates the number and type of roots of a quadratic equation.

• The discriminant indicates the maximum value of the quadratic function.

• The discriminant is used to find the vertex of the parabola.

• The discriminant determines the slope of the quadratic graph.

How can you determine if a quadratic function opens upwards or downwards?

• The sign of the coefficient 'a' in the quadratic function.

• The value of 'c' in the quadratic function.

• The number of roots of the quadratic function.

• The value of 'b' in the quadratic function.

What are the x-intercepts of a quadratic function?

• The x-intercepts are the values of y when x = 0.

• The x-intercepts are the maximum points of the graph.

• The x-intercepts are the coefficients of the quadratic equation.

• The x-intercepts are the solutions to the equation ax^2 + bx + c = 0.

How do you complete the square for a quadratic equation?

• Factor the equation into two linear terms.

• Graph the equation to find the vertex.

• Complete the square by rewriting ax^2 + bx + c as a(x + b/2a)^2 + (c - b^2/4a).

• Use the quadratic formula to find the roots.

What is the axis of symmetry in a quadratic function?

• x = -a/(2b)

• x = -b/(2a)

• x = 2a/b

• x = b/(2a)

How can you graph a quadratic function using its vertex and intercepts?

• Plot only the x-intercept and ignore the vertex.

• Draw a straight line connecting the intercepts.

• Graph the quadratic function by plotting the vertex and intercepts, then sketch a parabola through these points.

• Use only the vertex to create a point without a parabola.

What are the real-world applications of quadratic functions?

• Real-world applications of quadratic functions include projectile motion, profit maximization in economics, structural design in engineering, and population growth modeling in biology.

• Weather forecasting in meteorology

• Simple interest calculations in finance

• Linear regression in statistics