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Given the original formula the student enters the transformed formula
\nReady to use
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "{eqnline(a,b,x2,y2,v)}
\nThe Blue graph shows a graph of a quadratic equation, $f(x)=x^2$
\nThe Blue graph has been transformed onto the red graph $g(x)$, type in the new function definition:
\nThe Blue graph has been transformed onto the black graph $h(x)$, type in the new function definition:
\n", "advice": "We know that the graph crosses the $x$-axis at both $(\\var{a},0)$ and $(\\var{b},0)$. Since this is a quadratic, we know our equations has two roots, and by the previous observation, they are at $\\var{a}$ and $\\var{b}$. Hence we can write our equation as $\\simplify{y=(x-{a})(x-{b})}$ which simplifies to $\\simplify{y=x^2-({a}+{b})x+({a}*{b})}$.
\n\nTo find the coefficients of the turning point of the quadratic, we know the x-coordinate of the turning point will correspond to the solution to $dy/dx=0$. So we get $\\simplify{2x-({a}+{b})}=0$ hence $\\simplify{x=({a}+{b})/2}$. We substitute this value of x back into the equation of the quadratic to find the corresponding y-coordinate.
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\n$g(x)=\\;$[[0]]
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\n$h(x)=\\;$[[0]]
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