the vertex of the parabola formed from the quadratic equation y = x ^ 2 - 7x + 12

 Answer:-  To find the vertex of the parabola formed from the quadratic equation

$𝑦={𝑥}^2-7𝑥+12$, we can use the vertex formula for a parabola in the form $𝑦=𝑎{𝑥}^2+𝑏𝑥+𝑐$, which is given by:

$\text{Vertex }(ℎ,𝑘)=(-\frac{𝑏}{2𝑎},\frac{4𝑎𝑐-{𝑏}^2}{4𝑎})$

Comparing the given equation $𝑦={𝑥}^2-7𝑥+12$ with the general form $𝑦=𝑎{𝑥}^2+𝑏𝑥+𝑐$, we have:

• $𝑎=1$
• $𝑏=-7$
• $𝑐=12$

Substitute these values

h=−2(1)(−7)​=27​

$𝑘=\frac{4(1)(12)-(-7{)}^2}{4(1)}=\frac{48-49}{4}=-\frac{1}{4}$

Therefore, the vertex of the parabola formed by the quadratic equation is $(\frac{7}{2},-\frac{1}{4})$.