Properties of Parabolas Quiz

What is the value of c if the vertex of the function's graph is given as (-1,3) for the function y=c-x^2-2x?

Determine the vertex and the axis of symmetry for the function y = -4x^2 - 24x - 36.

What is the value of c if the vertex of the function's graph is given as (1,0) for the function y=-3x^2+6x+c?

What is the minimum value of the function for the graph of y=3x^2-12+13?

What is the maximum value of the function y=-3x^2+6x+5?

Identify the vertex and the axis of symmetry for the graph of y=x^2+3x+2.

What is the vertex and the axis of symmetry for the function y=4x^2 - 12x + 9?

What will be the longest side of the rectangular restaurant given 120 feet of fencing available for three sides?

What is the maximum area for the restaurant space with the fencing provided?

Properties of Parabolas

The vertex form of a parabola provides the highest or lowest point, critical for determining the shape and position of the graph.
For the function y=c-x²-2x with vertex (-1,3), the value of c is determined as 2.
The function y = -4x² - 24x - 36 has a vertex at (-3,0) and an axis of symmetry at x = -3.
In the equation y = -3x² + 6x + c, with vertex (1,0), the value of c is calculated to be -3.
In the function y = 3x² - 12 + 13, the minimum value of the function is found to be 1.
For the equation y = (1/2)x² + 2x - 8, specific values were highlighted without a detailed answer provided.
The maximum value of the function y = -3x² + 6x + 5 is determined to be 8, indicating a downward-opening parabola.
The vertex and axis of symmetry for the graph y = x² + 3x + 2 are at (-3/2, -1/4) and x = -3/2, respectively.
Analyzing y = -1/2x² - 2x + 1 results in an undefined conclusion marked as C).
The vertex and axis of symmetry for y = 4x² - 12x + 9 were evaluated with a conclusion designated as B).
A practical application involving fencing for a restaurant space revealed that with 120 feet of fencing allocated to three sides, the longest side measures 60 ft, yielding a maximum area of 1,800 square feet.

This quiz tests your understanding of the properties of parabolas, including their vertex forms, maximum and minimum values, and axes of symmetry. You will analyze various quadratic functions and determine their characteristics. Perfect for students learning about graphing and quadratic equations.