Answer:
The correct options are 1 and 4.
Step-by-step explanation:
The given function is
\(h(x)=x^2+20x-17\)
\(h(x)=(x^2+20x)-17\)
Add and subtract \((\frac{-b}{2a})^2\) in the parentheses
\((\frac{-b}{2a})^2=(\frac{-20}{2(1)})^2=100\)
\(h(x)=(x^2+20+100-100)-17\)
\(h(x)=(x^2+20+100)-100-17\)
\(h(x)=(x+10)^2-117\) ....(1)
The vertex form of the parabola is \(h(x)=(x+10)^2-117\). Option 2 is incorrect.
The general vertex form of a parabola is
\(f(x)=(x-h)^2+k\) ....(2)
Where, (h,k) is the vertex of the parabola.
On comparing (1) and (2) we get
\(h=-10\)
\(k=-117\)
Therefore the vertex of the function is (-10,-117). Option 1 is correct.
It is upward parabola, so the minimum value of the function is -117. Option 3 is incorrect.
The vertex of the function f(x)=x² is (0,0) and the vertex of h(x) is (-10,-117).
It means the f(x) shifts left by 10 units and down 117 units. Option 4 is correct.
The axis of symmetry of the function is x=h.
So, the axis of symmetry is
\(x=-10\)
Therefore option is x=-10. Option 5 is incorrect.
