Question

If $k > 4$ is a constant, how would you translate the graph of $y=x^{2}$ to get the graph of $y=x^{2}+4 x+k ?$ (A) left 2 units and up $k$ units (B) right 2 units and up $(k-4)$ units (C) left 2 units and up $(k-4)$ units (D) right 2 units and down $(k-4)$ units (E) left 2 units and down $(k-4)$ units

Name: Problem 46, Chapter 1: Math Level 2 SAT Subject Test
Uploaded: 2021-05-28T09:01:35-08:00
Duration: 6 min 9 s
Channel: Rahul Kumar
Description: If k > 4 is a constant, how would you translate the graph of y=x^2 to get the graph of y=x^2+4 x+k ? (A) left 2 units and up k units (B) right 2 units and up (k-4) units (C) left 2 units and up (k-4) units (D) right 2 units and down (k-4) units (E) left 2 units and down (k-4) units

   If $k > 4$ is a constant, how would you translate the graph of $y=x^{2}$ to get the graph of $y=x^{2}+4 x+k ?$
(A) left 2 units and up $k$ units
(B) right 2 units and up $(k-4)$ units
(C) left 2 units and up $(k-4)$ units
(D) right 2 units and down $(k-4)$ units
(E) left 2 units and down $(k-4)$ units

Math Level 2 SAT Subject Test

Richard Ku, Howard… 10th Edition

Chapter 1, Problem 46

Instant Answer

Solved by Expert Rahul Kumar

05/28/2021

Step 1

Step 1: We start with the function $y=x^{2}$. Show more…

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If $k > 4$ is a constant, how would you translate the graph of $y=x^{2}$ to get the graph of $y=x^{2}+4 x+k ?$ (A) left 2 units and up $k$ units (B) right 2 units and up $(k-4)$ units (C) left 2 units and up $(k-4)$ units (D) right 2 units and down $(k-4)$ units (E) left 2 units and down $(k-4)$ units

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Key Concepts

Vertex Form of a Quadratic

The vertex form of a quadratic function, written as y = a(x - h)² + k, directly reveals the vertex (h, k) of the parabola. This form is instrumental in understanding how the graph of the quadratic function has been translated from the standard form.

Completing the Square

Completing the square is an algebraic method used to transform a quadratic expression into a perfect square form plus a constant. This technique is crucial for rewriting quadratic equations into vertex form, making it easier to identify translations and the vertex of the parabola.

Graph Translation

Graph translation is the process of shifting a graph horizontally and/or vertically in the coordinate plane. This concept involves moving each point of the graph by a specified distance without altering the shape or orientation of the original graph.

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