Questions: Determine the quadratic function of the form f(x)=a(x-h)^2+k whose graph is given on the right. f(x)=

Transcript text: Determine the quadratic function of the form $f(x)=a(x-h)^{2}+k$ whose graph is given on the right. \[ f(x)= \]

Solution

Solution Steps

Step 1: Identify the Vertex

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

Step 2: Substitute the Vertex into the Vertex Form

The vertex form of a quadratic function is $ f(x) = a(x - h)^2 + k $. Substituting $ h = 2 $ and $ k = -5 $, we get: \[ f(x) = a(x - 2)^2 - 5 \]

Step 3: Use Another Point to Find 'a'

We use the point (1, 4) to find the value of 'a'. Substitute $ x = 1 $ and $ f(x) = 4 $ into the equation: \[ 4 = a(1 - 2)^2 - 5 \] \[ 4 = a(1)^2 - 5 \] \[ 4 = a - 5 \] \[ a = 9 \]

Final Answer

The quadratic function is: \[ f(x) = 9(x - 2)^2 - 5 \]

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