Maths Project Testing
∫ − 2 2 − 1 8 x 2 + 0.5 d x {\displaystyle \int _{-2}^{2}-{\frac {1}{8}}x^{2}+0.5\,dx}
f ( x ) = a x 2 + b x + c {\displaystyle f(x)=ax^{2}+bx+c\,}
f ( x ) = a x 2 + b x + c {\displaystyle f(x)=ax^{2}+bx+c}
f ( x ) = a ( x − p ) 2 + q {\displaystyle f(x)=a(x-p)^{2}+q}
x + p = 0 {\displaystyle x+p=0}
x = − p {\displaystyle x=-p}
b ± b 2 − 4 a c 2 a {\displaystyle {\frac {b\pm {\sqrt {b^{2}-4ac}}}{2a}}}
4 = a ( − 2 ) 2 + b ( − 2 ) + 4.5 {\displaystyle 4=a(-2)^{2}+b(-2)+4.5}
4 = 4 a − 2 b + 4.5 {\displaystyle 4=4a-2b+4.5}
4 = 4 a + 4.5 {\displaystyle 4=4a+4.5}
4 a = − 0.5 {\displaystyle 4a=-0.5}
a = − 1 8 {\displaystyle a={\frac {-1}{8}}}
y = 1 8 x 2 + 4.5 {\displaystyle y={\frac {1}{8}}x^{2}+4.5}
1 2 {\displaystyle {\frac {1}{2}}}
1 2 = 0 a 2 + 0 b + c {\displaystyle {\frac {1}{2}}=0a^{2}+0b+c}
c = 1 2 {\displaystyle c={\frac {1}{2}}}
y = 1 8 x 2 + 0.5 {\displaystyle y={\frac {1}{8}}x^{2}+0.5}
