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The parabola
y=x^(2) is shifted up by 7 units and to the left by 1 unit.
What is the equation of the new parabola?

y=

The parabola $y=x^{2}$ is shifted up by $7$ units and to the left by $1$ unit. $\newline$ What is the equation of the new parabola? $\newline$ $y=\square$

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Transformations of functions

Full solution

Q. The parabola

y=x^{2}

is shifted up by

7

units and to the left by

1

unit.

\newline

What is the equation of the new parabola?

\newline

y=\square

Shift up by $7$ units: To shift the parabola $y = x^2$ up by $7$ units, we add $7$ to the $y$ -value of the original equation. This gives us a new equation $y = x^2 + 7$ .
Shift left by $1$ unit: To shift the parabola to the left by $1$ unit, we replace $x$ with $(x + 1)$ in the equation. This is because moving to the left on the x-axis means increasing the x-value by $1$ . The new equation becomes $y = (x + 1)^2 + 7$ .

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