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Chapter 2: Q. 5 (page 76)

Find a so that the point $(- 1, 2)$ is on the graph of $f (x) = a x^{2} + 4$ .

Short Answer

Expert verified

The value of a is $- 2$ .

Step by step solution

Step 1. Given information

The given function is

$f (x) = a x^{2} + 4$

Need to find the value of $a$ so that the point $(- 1, 2)$ is on the graph.

Step 2. Solving for the value of a

Substitute $x = - 1$ and $f (x) = 2$ in the equation $f (x) = a x^{2} + 4$ ,

$\begin{array}{rcl} 2 & = & a {(- 1)}^{2} + 4 \\ 2 & = & a (1) + 4 \\ a & = & 2 - 4 \\ = & - 2 \end{array}$

The value of a is $- 2$ .

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Most popular questions from this chapter

If $f (x) = \{\begin{cases} x^{3} i f - 2 \leq x < 1 \\ 3 x + 2 i f 1 \leq x \leq 4 \end{cases}$

Find: (a) $f (- 1)$ (b) $f (0)$ (c) $f (1)$ (d) $f (3)$

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

$f (x) = {(x - 1)}^{3} + 2$

In Problems 7–18, match each graph to one of the following functions:

$A . y = x^{2} + 2 B . y = - x^{2} + 2 C . y = |x| + 2 D . y = - |x| + 2 E . y = {(x - 2)}^{2} F . y = - {(x + 2)}^{2} G . y = |x - 2| H . y = - |x + 2| I . y = 2 x^{2} J . y = - 2 x^{2} K . y = 2 |x| L . y = - 2 |x|$

A circle of radius ris in inscribed in a square. See the figure.

Part (a): Express the area A of the square as a function of the radius rof the circle.

Part (b): Express the perimeter p of the square as a function of the radius rof the circle.

If the domain of $f$ is all real numbers in the interval $[0, 7]$ and the domain of g is all real numbers in the interval $[- 2, 5]$ , the domain of $f + g$ is all real numbers in the interval _________.

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Find a so that the point -1,2is on the graph offx=ax2+4.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving for the value of a

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Most popular questions from this chapter

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Find a so that the point $(- 1, 2)$ is on the graph of $f (x) = a x^{2} + 4$ .