Equal outputs at two different inputs point to a parabola’s axis of symmetry, the vertical line that divides it into mirror images. Average those inputs to locate the axis. Then set it equal to the average of the two -intercepts and solve for the unknown in Desmos. Both pairs have the same midpoint. The trap is using a sum instead of an average.
Hints
- Hint 1
A parabola gives the same output at inputs equally far from its axis of symmetry, its vertical mirror line. The inputs here have equal outputs. What number lies halfway between them?
- Hint 2
An -intercept has output . The two intercept inputs also have equal outputs and lie equally far from the axis. How would you write their average using ?
- Hint 3
Set the two midpoints equal. To solve for in Desmos, replace with . If Desmos reports a decimal under PARAMETERS, type on its own line to get a fraction button.
Step-by-step
Match the two midpoints
Step 1Find the axis from the equal outputs
Because , the inputs and have equal outputs. A parabola mirrors equal-height points across its axis of symmetry, the vertical line through its turning point. So the axis is halfway between these inputs:
- Step 2
Set the intercepts’ midpoint equal to the axis
An -intercept is a point where the output is . So the intercept inputs and also mirror across that same axis, :
Don’t set these inputs equal to and . The problem says those inputs have equal outputs, not that their outputs are .
- Step 3
Solve for the intercept parameter
Type . The tells Desmos to find the unknown constant ; under PARAMETERS, it shows . Type on the next line and use the fraction button to see . So the value of is . Choice D.