the\ function\ h\left(x\right)=\frac{1}{2}\left(x+3\right)^{2}+2.How\ is\ the\ graph\ of\ h\left(x\right)\ t\ r\ a\ nslated\ \ from\ the\ parent\ graph\ of\ a\ quadratic\ function,\ f\left(x\right)=x^{2}

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05-02-2020
Mathematics

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the\ function\ h\left(x\right)=\frac{1}{2}\left(x+3\right)^{2}+2.How\ is\ the\ graph\ of\ h\left(x\right)\ t\ r\ a\ nslated\ \ from\ the\ parent\ graph\ of\ a\ quadratic\ function,\ f\left(x\right)=x^{2}

$the function hleftxrightfrac12leftx3right22How is the graph of hleftxright t r a nslated from the parent graph of a quadratic function fleftxrightx2 class=$

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vijayalalitha vijayalalitha · Answer 1 · 2020-02-13T10:40:03+01:00

The function h(x) is vertically stretched by a factor of [tex]\frac{1}{2}[/tex] and is shifted 3 units to the left and shifted 2 units up.

Explanation:

The parent function is [tex]f(x)=x^{2}[/tex]

The translated function is [tex]h(x)=\frac{1}{2}(x+3)^{2}+2[/tex]

By using the function transformation rules, the translated function h(x) is stretched vertically by a factor of [tex]\frac{1}{2}[/tex]

Also, from the function transformation rules, we know that, [tex]$f(x+b)$[/tex] shifts the function b units to the left.

Thus, the translated function h(x) is shifted 3 units to the left.

By using the function transformation rules, we know that, [tex]$f(x)+b$[/tex] shifts the function b units upward.

Thus, the translated function h(x) is shifted 2 units upwards.

Thus, the translated function h(x) is vertically stretched by a factor of [tex]\frac{1}{2}[/tex] and is shifted 3 units to the left and shifted 2 units up.