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What is the vertex of the following function? y=-4vert x+2vert +5 (2,5) (-2,5) (-4,2) (-4,-2)

Pergunta

What is the vertex of the following function?
y=-4vert x+2vert +5
(2,5)
(-2,5)
(-4,2)
(-4,-2)

What is the vertex of the following function? y=-4vert x+2vert +5 (2,5) (-2,5) (-4,2) (-4,-2)

Solução

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LeonardoProfissional · Tutor por 6 anos

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The vertex of the function is (-2,5).

Explicação

## Step 1<br />The given function is \(y=-4\vert x+2\vert +5\). This is an absolute value function, which is a transformation of the basic absolute value function \(y=\vert x\vert\).<br /><br />## Step 2<br />The absolute value function \(y=\vert x\vert\) has its vertex at the origin (0,0). When the function is transformed, the vertex also moves.<br /><br />## Step 3<br />In the given function, the absolute value function is transformed by shifting 2 units to the left and 5 units up. This is due to the "+2" inside the absolute value function and the "+5" outside the absolute value function.<br /><br />## Step 4<br />The negative sign in front of the 4 indicates a reflection over the x-axis.<br /><br />## Step 5<br />Therefore, the vertex of the function \(y=-4\vert x+2\vert +5\) is at (-2,5).
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