# Graphing Parabolas

Graphing parabolas is a fundamental concept in algebra and geometry that involves plotting and analyzing quadratic functions. Parabolas, which are U-shaped curves, are defined by their vertex, axis of symmetry, and direction of opening. Understanding how to graph parabolas allows us to visualize their behavior, identify key features such as the vertex and intercepts, and solve various mathematical problems. Whether in quadratic equations, projectile motion, or optimization problems, mastering the art of graphing parabolas is essential for students and professionals alike in fields such as mathematics, physics, engineering, and computer science.

Questions

- What is the graph of #f(x)=-2x^2+7x+4#?
- How do you identity if the equation #x^2+y^2+6y+13=40# is a parabola, circle, ellipse, or hyperbola and how do you graph it?
- How do you find the vertex, focus, and directrix of the following parabola and graph the equation #y^2-8y+8x+16=0#?
- How do I make a parabola with the function y=1/2x^2 with the values -2, -1, 0, 1, 2?
- What is the parent graph of a parabola?
- How do I find the axis of the graph of the function #f(x)=4x^2+8x+7#?
- What is the graph of the parabola represented by #y=2x^2-8x+9#?
- What is the x-intercept of the graph of #y=x^2-4x+4#?
- What is the vertex of the graph of #y=x^2+3x-4#?
- How do you identity if the equation #x^2-8y+y^2+11=0# is a parabola, circle, ellipse, or hyperbola and how do you graph it?
- What is the vertex of the graph of #y=2(x-3)^2-7#?
- What is the vertex of the graph of #y=-(x-2)^2+3#?
- What is the axis of symmetry of the graph of #y=-(x+3)^2-6#?
- How do I graph #y=x^2-2x-3#?
- How do I graph #y=x^2-9#?
- How do I graph #y=x^2-6x+5#?
- How do I find the x-intercepts for the graph of #y=x^2+4x-5#?
- How do I find the x-intercepts for the graph of #y=x^2-3x-4#?
- How do I find the x-intercepts of the graph of #y=x^2+2x-8#?
- How do you identity if the equation #x^2+2y^2=2x+8# is a parabola, circle, ellipse, or hyperbola and how do you graph it?