Pregunta
Re-write the quadratic function below in Standard Form \[ y=-2(x-4)^{2}+8 \]
Ask by Schneider Schultz. in the United States
Feb 19,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The standard form of the quadratic function is \( y = -2x^{2} + 16x - 24 \).
Solución
To rewrite the quadratic function \( y = -2(x-4)^{2} + 8 \) in standard form, we need to expand the expression and simplify it. The standard form of a quadratic function is given by:
\[
y = ax^2 + bx + c
\]
where \( a \), \( b \), and \( c \) are constants.
Let's proceed step by step:
1. **Expand the squared term**:
\[
(x-4)^{2} = x^{2} - 8x + 16
\]
2. **Substitute back into the equation**:
\[
y = -2(x^{2} - 8x + 16) + 8
\]
3. **Distribute \(-2\)**:
\[
y = -2x^{2} + 16x - 32 + 8
\]
4. **Combine like terms**:
\[
y = -2x^{2} + 16x - 24
\]
Now, we have the quadratic function in standard form:
\[
y = -2x^{2} + 16x - 24
\]
Thus, the standard form of the given quadratic function is:
\[
y = -2x^{2} + 16x - 24
\]
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Simplifique esta solución The Deep Dive
To convert the quadratic function from vertex form to standard form, we start with: \[ y = -2(x-4)^{2} + 8 \] First, expand the squared term: \[ (x-4)^{2} = x^2 - 8x + 16 \] Now substitute this back into the equation: \[ y = -2(x^2 - 8x + 16) + 8 \] Distributing \(-2\) gives: \[ y = -2x^2 + 16x - 32 + 8 \] Now, combine the constant terms: \[ y = -2x^2 + 16x - 24 \] So the quadratic function in standard form is: \[ y = -2x^2 + 16x - 24 \]
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