Complete the square on the right side of the equation.
Use the form ax^2 + bx + cax^2 + bx + c, to find the
values of aa , bb, and cc.
a<span>=1, b</span><span>=4, c</span><span>=7</span>
Consider the vertex form of a parabola.
a(x + d)^<span>2 </span>+ e
Find the value of <span>d<span> using
the formula <span>d =<span><span> b</span><span><span> / 2</span>a</span></span></span></span></span>
Multiply <span>2<span> by <span>1<span> to
get <span><span>2 ⋅ 1</span>.</span></span></span></span></span>
<span>d =
4 / (2 * 1)</span>
d = 2
<span>
</span>
Find the value of <span>e<span> using
the formula <span><span>e =</span><span><span>c<span> −</span></span><span>b<span><span>^2 / 4</span>a</span></span></span></span></span></span>
<span>
</span>
Multiply <span>4<span> by <span>1<span> to
get <span>4 ⋅ 1</span></span></span></span></span>
E =<span> 7<span> – ((4)</span></span><span>^2</span><span> / (4 ⋅ 1</span>))
Reduce the expression by cancelling the common factors.
E =<span> 7<span> – 1 ⋅ 4</span></span>
Subtract 44 from 77 to get 33.
e = 3
Substitute the values
of a, d, and e into the vertex form a(x + d)^2 + e.
(x <span>+ 2)</span>^2 + 3
Therefore, the vertex form of the quadratic equation is:
<span>
</span>
y =<span><span> (<span><span>x + 2</span>)</span></span><span>^2 + 3</span></span>