Question

HELP !!!! can someone help me please how can i use the vertex formula to find this equation for this graph ?

Answer 1

based on that table of values, we know the highest point(vertex) is at 0.9, 5.9

we can also use just one another point... say 1.4, 4.6


`\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} y=a(x-{{ h}})^2+{{ k}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\`


`\bf \begin{cases} h=0.9\\ k=5.9 \end{cases}\implies y=a(x-0.9)^2+5.9 \\\\\\ \begin{cases} \textit{another point}\\ x=1.4\\ y=4.6 \end{cases}\implies 4.6=a(1.4-0.9)^2+5.9 \\\\\\ 4.6=a(0.5)^2+5.9\implies 4.6-5.9=a(0.5)^2\implies -1.3=a(0.5)^2 \\\\\\ \cfrac{-1.3}{0.5^2}=a\implies -5.2=a \\\\\\ thus\qquad \qquad \boxed{y=-5.2(x-0.9)^2+5.9}`