Problem 8 of 34fun-008
In the standard (x,y) coordinate plane, what is the vertex of the parabola y=2x2−8x+3?
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Solution walkthrough1:36
- The vertex is the turning point. For y=ax2+bx+c its x-coordinate is x=−2ab.
- With a=2 and b=−8: x=−2(2)−8=48=2.
- Put x=2 into the equation: y=2(2)2−8(2)+3=8−16+3=−5.
- The vertex is (2,−5). Check: x=0 and x=4 are each 2 away and both give y=3.
- Traps: (2,3) uses c for y; (−2,27) loses a minus sign; (4,3) forgets the 2 in 2a.