find the standard form of this vertex form of this quadratic function
y=(x+4)^2-16
thank you..with steps please
The standard form of a quadratic equation:
y = a x² + b x + c
in this case:
y = ( x + 4 )² - 16
Apply perfect square formula for ( x + 4 )²
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( a + b )² = a² + 2 ∙ a ∙ b + b²
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( x + 4 )² = x² + 2 ∙ x ∙ 4 + 4² = x² + 8 x + 16
Replace ( x + 4 )² = x² + 8 x + 16 in your equation:
y = ( x + 4 )² - 16 = x² + 8 x + 16 - 16
y = x² + 8 x
Well, well, well, looks like we have a quadratic function in vertex form hiding here! Let's transform it into the standard form, shall we?
Step 1: Multiply out the square.
We start by expanding the parentheses. Don't worry, math isn't like clown cars - it won't scare you!
y = (x + 4)(x + 4) - 16
Step 2: Simplify the equation.
Apply some distribution magic and perform the math:
y = x^2 + 8x + 16 - 16
Step 3: Combine like terms.
Now, let's add and subtract, because our quadratic function is getting pretty complex!
y = x^2 + 8x
Voila! We successfully transformed the quadratic function from vertex form to standard form. Now it looks all official and majestic. Your function in standard form is y = x^2 + 8x. Enjoy your quadratic journey!
To convert the quadratic function given in vertex form, y = (x + h)^2 + k, into standard form, y = ax^2 + bx + c, where a, b, and c are constants, follow these steps:
Step 1: Identify the values of h and k from the vertex form.
In the given function, y = (x + 4)^2 - 16, the value of h is -4, and the value of k is -16.
Step 2: Expand the square.
(x + 4)^2 = (x + 4)(x + 4) = x^2 + 4x + 4x + 16 = x^2 + 8x + 16
Step 3: Substitute the expanded expression and the values of h and k into the standard form.
y = (x + 4)^2 - 16
y = x^2 + 8x + 16 - 16
y = x^2 + 8x
So, the standard form of the given quadratic function is y = x^2 + 8x.
To find the standard form of the vertex form quadratic function y = (x + h)^2 + k, where (h, k) represents the vertex, follow these steps:
Step 1: Expand the squared term using the rule (a + b)^2 = a^2 + 2ab + b^2.
Expanding (x + 4)^2 gives:
y = x^2 + 2(4)x + 4^2 - 16
Simplifying further:
y = x^2 + 8x + 16 - 16
Step 2: Combine like terms:
y = x^2 + 8x
So, the standard form of the given quadratic function y = (x + 4)^2 - 16 is y = x^2 + 8x.