Can someone please explain to me how I am supposed to Reflect Quadratic Functions with and without a graph??
I’ve missed a handful of school days because of personal reasons / family emergencies and i need to catch up but I have no clue how to do the work.
with a graph, just draw the axis of reflection, and fold the paper over along that line and trace the curve; then unfold the paper.
algebraically, see this nice article in wikipedia:
http://www.sdmath.com/math/geometry/reflection_across_line.html#formulasmb
my email is gravityfive459 if it will be easier to just see the problems and help me out. if you decide to email me just make the subject “algebra help” so i know to open it :)
I'm sorry to hear that you've missed some school days, but I'm here to help you catch up on reflecting quadratic functions. To reflect a quadratic function, both with and without a graph, you'll need to understand the basic concepts and steps involved. Here's how you can approach it:
Reflecting Quadratic Functions with a Graph:
1. Identify the original quadratic function in vertex form. The general equation is f(x) = a(x-h)^2 + k, where (h,k) represents the vertex of the parabola.
2. Determine the axis of symmetry by finding the x-coordinate of the vertex, which is -h in the equation.
3. Create a mirror image of the original graph by reflecting it across the axis of symmetry. This means that any point (x,y) on the original graph will have a corresponding point (2h-x, y) on the reflected graph.
4. The resulting graph after reflecting the quadratic function will still be a parabola, but facing in the opposite direction, assuming the original graph was concave up (U-shaped) or concave down (n-shaped).
Reflecting Quadratic Functions without a Graph:
1. Identify the original quadratic function in vertex form, which is f(x) = a(x-h)^2 + k.
2. Find the vertex (h,k) of the original parabola.
3. Reflect the vertex across the x-axis by changing the sign of the y-coordinate, resulting in a new vertex (h, -k).
4. Rewrite the quadratic function with the new vertex, f(x) = a(x-h)^2 - k. This will be the equation for the reflected parabola.
Remember, the value of 'a' in the quadratic equation affects the steepness and scale of the parabola. Additionally, a negative value of 'a' will cause the graph to be reflected along the x-axis.
I hope this explanation helps you understand how to reflect quadratic functions both with and without a graph. If you have any further questions, feel free to ask!