Question

Rewrite the quadratic function f(x)=x^2-3x+2 into standard form. Identify its vertex and all its intercepts.

Answer 1

Given

$f\mleft(x\mright)=x^2-3x+2$

Find

Rewrite it into standard form and identify vertex and all its intercepts.

Explanation

standard form =

$f(x)=a(x-h)^2+k$

where (h , k) be the vertex

so ,

$\begin{gathered} f(x)=x^2-3x+2 \\ x^2-3x+\frac{9}{4}=-2+\frac{9}{4} \\ (x-\frac{3}{2})^2=\frac{1}{4} \\ f(x)=(x-\frac{3}{2})^2-\frac{1}{4} \\ \end{gathered}$

so vertex be

$(\frac{3}{2},-\frac{1}{4})$

for intercept put f(x) = 0

$\begin{gathered} x^2-3x+2=0 \\ (x-1)(x-2)=0 \\ x=1,2 \end{gathered}$

so , x - intercept = (1 , 0) and (2 , 0)

for y- intercept put x =0

$\begin{gathered} y=(0)^2-3(0)+2 \\ y=2 \end{gathered}$

y - intercept (0 , 2)

Final Answer

Therefore , vertex is (3/2,-1/4)

x - intercept = (1 , 0) and (2 , 0) and y - intercept (0 , 2)