# Quadratic Functions and Their Graphs

Quadratic functions play a pivotal role in algebra and mathematics, offering a powerful tool to analyze and understand various real-world phenomena. Defined by the standard form ax^2 + bx + c, these functions generate parabolic graphs that depict a wide range of scenarios, from projectile motion to economic modeling. The study of quadratic functions and their graphs encompasses fundamental concepts such as vertex analysis, axis of symmetry, and solutions to quadratic equations. This exploration not only aids in problem-solving but also provides a foundational understanding of the intricate relationships between variables in mathematical expressions.

Questions

- How do you graph #x = (5/2)y^2# on a graphing calculator?
- What is the vertex of # y= 3x^2+x+6+3(x-4)^2#?
- How do you find the axis of symmetry, and the maximum or minimum value of the function #y = 4x^2 + 5x – 1#?
- How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #y = x^2 - 2x - 15#?
- What is the the vertex of #y =-4x^2+2x+1 #?
- Determine the critical points and draw the graph of #y=2x^2# ?
- What is the the vertex of #y = 3x^2 -6x +8#?
- How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #y=-x^2+3x-3#?
- What is the axis of symmetry and vertex for the graph #f(x) = -3x^2 + 3x - 2#?
- How do you find the maximum or minimum of #y-x^2+6=9x#?
- How do you graph #f(x)=1/2x^2 +2x - 8#?
- What is the vertex of #y= (x − 3)(4x + 2) #?
- What are the coordinates of the vertex of y = x^2-2x-7?
- How do you graph #y= -x^2 + 5#?
- What is the vertex of #y=(x-4) (x+2)#?
- How do you find the axis of symmetry, and the maximum or minimum value of the function #y = x^2 - 4x + 1#?
- How do you graph the parabola #y=-x^2-10x-20# using vertex, intercepts and additional points?
- What is the equation of the axis of symmetry for #y=x^2-25#??
- What is the minimum or maximum of #g(x)=-x^2-6x+1#?
- How do you find the vertex and axis of symmetry, and then graph the parabola given by: #f(x)=2x^2-4x+1#?