Question

Find the rule of the quadratic function whose graph has its vertex at (2, 1) and passes through (1, 4).

Answer 1

have you covered parabolas yet?

Answer 2

yes

Answer 3

ok

Answer 4

\(\bf y = a(x-{\color{blue}{ h}})^2+{\color{red}{ k}}\qquad vertex\ (2,1)\implies y = a(x-{\color{blue}{ 2}})^2+{\color{red}{ 1}}\)

so what's "a"? we dunno, but we know that the parabola passes through (1,4)
meaning that when x = 1, y = 4

thus \(\bf through \quad ({\color{green}{ 1, 4}})\quad
y = a(x-{\color{blue}{ 2}})^2+{\color{red}{ 1}}\implies {\color{green}{ 1}} = a({\color{green}{ 2}}-{\color{blue}{ 2}})^2+{\color{red}{ 1}}\)

solve for "a" to find the factor "a", then plug it into the equation

Answer 5

can u please factor a