How do you write y=1.4x2+5.6x+3 in vertex form?

1 Answer
Shell
Sep 19, 2016

y=1.4(x+2)2−2.6

Explanation:

y=1.4x2+5.6x+3 is in the form y=ax2+bx+c

To find the x coordinate of the vertex, use the formula x=−b2a

x=−b2a=−5.62⋅1.4=−2

To find the y coordinate of the vertex, plug x=−2 into the equation.

y=1.4(−2)2+5.6(−2)+3=−2.6

The vertex is (−2,−2.6)

Use the formula for the vertex form of a quadratic.
y=a(x−h)2+k where (h,k) is the vertex.
y=a(x+2)2−2.6

To find the constant a, find a convenient point that satisfies the original equation. Typically, the y intercept is found, because the algebra is simple. In other words, find y when x=0.

y=1.4(0)2+5.6(0)+3=3
Thus, a point that satisfies the equation is (0,3)

Use this point to find a by substituting it into the equation for the vertex.
3=a(0+2)2−2.6
3=4a−2.6
5.6=4a
a=1.4

Substituting 1.4 for a into the vertex form equation gives
y=1.4(x+2)2−2.6

There is another process for converting standard form to vertex form called completing the square. If you need to learn this method, please comment, and I will add it to the answer.

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