Question

4.4.1 study: transformation of parent functions
what is the equation of the
function graphed?
\\( f(x) = x^2 + 3 \\)
\\( f(x) = 3x^2 \\)
\\( f(x) = (x + 3)^2 \\)
\\( f(x) = (x - 3)^2 \\)
4 of 8
submit

Explanation:

Step1: Recall vertex form of parabola

The parent function of a parabola is \( y = x^2 \), with vertex at \((0,0)\). For a function \( y=(x - h)^2+k \), the vertex is \((h,k)\).

Step2: Analyze the graph's vertex

From the graph, the vertex of the parabola \( F(x) \) is at \((- 3,0)\) (since it's on the x - axis, \( y = 0\) and shifted left).

Step3: Match with the given options

• For \( F(x)=x^{2}+3 \), the vertex is \((0,3)\), which does not match.
• For \( F(x) = 3x^{2}\), the vertex is \((0,0)\), which does not match (the graph is shifted left).
• For \( F(x)=(x + 3)^{2}\), using the vertex form \( y=(x - h)^2+k \), here \( h=-3,k = 0\), so the vertex is \((-3,0)\), which matches the graph.
• For \( F(x)=(x - 3)^{2}\), the vertex is \((3,0)\), which does not match.

Answer:

\( F(x)=(x + 3)^{2} \) (the option corresponding to this equation, e.g., if the third option is \( F(x)=(x + 3)^{2} \), then the answer is the option with \( F(x)=(x + 3)^{2} \))