Q 73. The graph of the function fx=ax2... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 3: Q 73. (page 157)

The graph of the function $f (x) = a x^{2} + b x + c$ has vertex at $(0, 2)$ and passes through the point $(1, 8)$ . Find $a, b$ and $c$ .

Short Answer

Expert verified

The solutions are $a = 6, b = 0$ , and $c = 2$ .

Step by step solution

Step 1. Given information.

Given function $f (x) = a x^{2} + b x + c$ .

Vertex at $(0, 2)$ and passes through the point $(1, 8)$ .

Step 2. Determine the value of b and c.

The coordinates of the vertex of a quadratic function of the form $f (x) = a x^{2} + b x + c$ are role="math" localid="1646894449869" $(\frac{- b}{2 a}, f (\frac{- b}{2 a}))$ .

So, $(\frac{- b}{2 a}, f (\frac{- b}{2 a})) = (0, 2) 鈰� 鈰� (G i v e n v e r t e x (0, 2))$ .

$\begin{array}{rcl} \frac{- b}{2 a} & = & 0 \\ - b & = & 0 \\ b & = & 0 \end{array}$ and $\begin{array}{rcl} f (\frac{- b}{2 a}) & = & 2 \\ f (0) & = & 2 鈰� 鈰� (\frac{- b}{2 a} = 0) \\ a {(0)}^{2} + b (0) + c & = & 2 鈰� 鈰� (s u b s t i t u t e x = 0 i n f (x) = a x^{2} + b x + c) \\ c & = & 2 \end{array}$

Step 3. Determine the value of a.

From the point $(1, 8)$ , we find that $f (1) = 8$ .

Substitute $1$ for $x$ , $0$ for $b$ , $2$ for $c$ , and $8$ for $f (1)$ in $f (x) = a x^{2} + b x + c$ .

$\begin{array}{rcl} f (x) & = & a x^{2} + b x + c \\ f (1) & = & a {(1)}^{2} + 0 (1) + 2 \\ 8 & = & a + 2 \\ a + 2 & = & 8 \\ a & = & 8 - 2 \\ a & = & 6 \end{array}$

Step 4. Simplified answer.

Hence, $a = 6, b = 0$ , and $c = 2$ .

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x	$y = f (x)$
-2	4
-1	1
0	-2
1	-5
2	-8

91影视

The graph of the function $f (x) = a x^{2} + b x + c$ has vertex at $(0, 2)$ and passes through the point $(1, 8)$ . Find $a, b$ and $c$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the value of b and c.

Step 3. Determine the value of a.

Step 4. Simplified answer.

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91影视

The graph of the function fx=ax2+bx+chas vertex at 0,2and passes through the point 1,8. Finda,bandc.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the value of b and c.

Step 3. Determine the value of a.

Step 4. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

The graph of the function $f (x) = a x^{2} + b x + c$ has vertex at $(0, 2)$ and passes through the point $(1, 8)$ . Find $a, b$ and $c$ .