Questions: Convert y=4(x+3)^2+5 to standard form. Enter your answer in the box. y=

Transcript text: Convert $y=4(x+3)^{2}+5$ to standard form. Enter your answer in the box. \[ y= \]

Solution

Solution Steps

To convert the given quadratic equation from vertex form to standard form, we need to expand the equation and simplify it. The vertex form of a quadratic equation is given by $ y = a(x-h)^2 + k $. We will expand $ (x+3)^2 $, multiply by 4, and then add 5 to get the standard form $ y = ax^2 + bx + c $.

Step 1: Expand the Squared Term

First, we expand the squared term in the given equation $ y = 4(x+3)^2 + 5 $: \[ (x+3)^2 = x^2 + 6x + 9 \]

Step 2: Multiply by the Coefficient

Next, we multiply the expanded term by 4: \[ 4(x^2 + 6x + 9) = 4x^2 + 24x + 36 \]

Step 3: Add the Constant Term

Finally, we add the constant term 5 to the result: \[ 4x^2 + 24x + 36 + 5 = 4x^2 + 24x + 41 \]