How do you write the quadratic function in standard form $y = 4 {(x - 1)}^{2} + 5$ ?

Open in App

Solution

Convert to standard form:
The standard form of the quadratic equation is $y = a x^{2} + b x + c; a \neq 0$
Expand the given equation and simplify:
$\begin{array}{rcl} y & = & 4 {(x - 1)}^{2} + 5 \\ = & 4 (x^{2} - 2 x + 1) + 5 [∵ {(a - b)}^{2} = a^{2} + b^{2} - 2 a b] \\ = & 4 x^{2} - 8 x + 4 + 5 \\ = & 4 x^{2} - 8 x + 9 \end{array}$
Therefore, the standard form of the given quadratic function is $y = 4 x^{2} - 8 x + 9$ .

Suggest Corrections

Similar questions

How do you write $4 x - y - 7 = 0$ in slope intercept form?

How do you write $y - 2 = - \frac{1}{2} (x - 4)$ in standard form?

How do you write $1.98 \times 10^{- 4}$ in standard form.

How do you write $x^{2} - 2 x = 8$ in standard form?

Join BYJU'S Learning Program