Find the Vertex 1.2x^2-4.3x-3.7

$1.2 x^{2} - 4.3 x - 3.7$

Step 1

Rewrite the equation in vertex form.

Complete the square for $1.2 x^{2} - 4.3 x - 3.7$ .

Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = 1.2$

$b = - 4.3$

$c = - 3.7$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e$

Find the value of $d$ using the formula $d = \frac{b}{2 a}$ .

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = \frac{- 4.3}{2 \cdot 1.2}$

Simplify the right side.

Multiply $2$ by $1.2$ .

$d = \frac{- 4.3}{2.4}$

Divide $- 4.3$ by $2.4$ .

$d = - 1.791\overline{6}$

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

Substitute the values of $c$ , $b$ and $a$ into the formula $e = c - \frac{b^{2}}{4 a}$ .

$e = - 3.7 - \frac{{(- 4.3)}^{2}}{4 \cdot 1.2}$

Simplify the right side.

Simplify each term.

Raise $- 4.3$ to the power of $2$ .

$e = - 3.7 - \frac{18.49}{4 \cdot 1.2}$

Multiply $4$ by $1.2$ .

$e = - 3.7 - \frac{18.49}{4.8}$

Divide $18.49$ by $4.8$ .

$e = - 3.7 - 1 \cdot 3.85208\overline{3}$

Multiply $- 1$ by $3.85208\overline{3}$ .

$e = - 3.7 - 3.85208\overline{3}$

Subtract $3.85208\overline{3}$ from $- 3.7$ .

$e = - 7.55208\overline{3}$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $1.2 {(x - 1.791\overline{6})}^{2} - 7.55208\overline{3}$ .

$1.2 {(x - 1.791\overline{6})}^{2} - 7.55208\overline{3}$

Set $y$ equal to the new right side.

$y = 1.2 {(x - 1.791\overline{6})}^{2} - 7.55208\overline{3}$

Step 2

Use the vertex form, $y = a {(x - h)}^{2} + k$ , to determine the values of $a$ , $h$ , and $k$ .

$a = 1.2$

$h = 1.791\overline{6}$

$k = - 7.55208\overline{3}$

Step 3

Find the vertex $(h, k)$ .

$(1.791\overline{6}, - 7.55208\overline{3})$

Step 4

Find the Vertex 1.2x^2-4.3x-3.7

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