The equation we are given (−at2+bt+c) is a parabola and we are told to describe what happens when we change c (the y-intercept).
hardest question
y=-at^2+bt+c
change c? if c is +, it moves the parabola up on the y,t graph.
If this is the hardest question you get on the practice ACT, you must have skipped many others.
can anyone answer this besides bobpursly
To understand what happens when we change the value of "c" in the equation of a parabola (−at^2 + bt + c), let's start by understanding the role of "c" in the standard form of a quadratic equation.
In general, the standard form of a quadratic equation is expressed as follows:
y = ax^2 + bx + c
"c" represents the y-intercept of the parabola, meaning the point where the parabola intersects the y-axis. It is the value of "y" when "x" is zero.
When we change the value of "c," we essentially shift the entire parabola vertically up or down. Here's what happens:
1. If "c" is positive:
- If c > 0, the parabola will move upward, shifting higher on the y-axis. This means the vertex of the parabola will be above its original position.
- The higher the value of "c" (positive), the more upward the parabola shifts.
2. If "c" is negative:
- If c < 0, the parabola will move downward, shifting lower on the y-axis. This means the vertex of the parabola will be below its original position.
- The lower the value of "c" (negative), the more downward the parabola shifts.
3. If "c" is zero:
- If c = 0, the y-intercept of the parabola is at the origin (0, 0). In this case, the parabola passes through the origin, and the vertex remains unchanged.
Remember, changing the value of "c" affects the vertical position of the parabola. Other properties such as the direction, width, and shape of the parabola are primarily influenced by the coefficients "a" and "b" in the quadratic equation.