KöMaL 2020 C1620

Jack Russell fashioned a springboard in his back yard. He carried out measurements to determine that by bending the springboard $x$ decimetres below horizontal, he could jump to a height of $0.5x^2+ax+b$ decimetres. Unfortunately, he forgot the values of $a$ and $b$. He only remembers that bending by $10$ cm let him jump $35$ cm, and a deformation four times as large resulted in a jump four times as high. What may have been Jack's measured values of $a$ and $b$?