y=2x^2+7x+3 is a quadratic equation in standard form:
y=ax^2+bx+c, where a=2, b=7, and c=3.
The vertex form is y=a(x-h)^2+k, where (h,k) is the vertex.
In order to determine h from the standard form, use this formula:
h=x=(-b)/(2a)
h=x=(-7)/(2*2)
h=x=-7/4
To determine k, substitute the value of h for x and solve. f(h)=y=k
Substitute -7/4 for x and solve.
k=2(-7/4)^2+7(-7/4)+3
k=2(49/16)-49/4+3
k=98/16-49/4+3
Divide 98/16 by color(teal)(2/2
k=(98-:color(teal)(2))/(16-:color(teal)(2))-49/4+3
Simplify.
k=49/8-49/4+3
The least common denominator is 8. Multiply 49/4 and 3 by equivalent fractions to give them a denominator of 8.
k=49/8-49/4xxcolor(red)(2/2)+3xxcolor(blue)(8/8
k=49/8-98/8+24/8
k=-25/8
The vertex form of the quadratic equation is:
y=2(x+7/4)^2-25/8
graph{y=2x^2+7x+3 [-10, 10, -5, 5]}
