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Select 2 key attributes that are true about the quadratic below: f(x)=-x^2-2x+3

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Select 2 key attributes that are true about the quadratic below:
f(x)=-x^2-2x+3

Select 2 key attributes that are true about the quadratic below: f(x)=-x^2-2x+3

Solución

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Arlettemaestro · Tutor durante 5 años
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The quadratic function \(f(x) = -x^2 - 2x + 3\) has a negative leading coefficient, which means the parabola opens downwards. The vertex of the parabola is (-1, 4).

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## Step 1<br />The given function is a quadratic function, which is a polynomial of degree 2. The general form of a quadratic function is \(f(x) = ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants, and \(a\) is not equal to zero.<br /><br />## Step 2<br />In the given function \(f(x) = -x^2 - 2x + 3\), the coefficient of \(x^2\) is negative, which means the parabola opens downwards.<br /><br />## Step 3<br />The vertex of the parabola is given by the formula \(-b/2a\). Substituting the values of \(a\) and \(b\) from the given function, we get \(-(-2)/2(-1) = -1\). Substituting \(x = -1\) in the function, we get \(f(-1) = -(-1)^2 - 2(-1) + 3 = 4\). So, the vertex of the parabola is (-1, 4).
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