Question

Write a quadratic function h whose only zero is 1

Answer 1

Answer:

x^2-2x+1

this factors out to (x-1)(x-)

both of those are equal to x=1

Answer 2

Answer:

$x^{2}-2x+1$

Step-by-step explanation:

1)A quadratic function with only one zero, i.e. root, must have its Δ =0.$\Delta =b^{2}-4ac$

2) $x^{2}-2x+1$

3) Solving by the Quadratic Formula:

$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}=\frac{-(-2)\pm \sqrt{4-4(1)(1)}}{2(1)}=\frac{2\pm \sqrt{0}}{2}=1 \Rightarrow S=\left \{ 1 \right \}$

4) Alternatively, solving by factoring:

$x^{2}-2x+1=(x-1)^2=(x-1)(x-1)\Rightarrow S=\left \{ 1 \right \}$

For 1 - 1 is equal to zero.