Q 74. 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 74. (page 157)

The graph of the function $f (x) = a x^{2} + b x + c$ has vertex at $(1, 4)$ and passes through the point $(- 1, - 8)$ . Findrole="math" localid="1646894617982" $a, b$ and $c$ .

Short Answer

Expert verified

$a = - 3, b = 6, c = 1$

Step by step solution

Step 1. Given information.

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

Given the vertex $(1, 4)$ and a point $(- 1, - 8)$ .

Step 2. Determine the value of a.

The vertex of a parabola is $(h, k) = (1, 4)$ . So, $h = 1$ and $k = 4$ .

The vertex form of the parabola is:

$f (x) = a {(x - h)}^{2} + k$

We know that one additional point $(- 1, - 8)$ .

So, $x = - 1$ and $\begin{array}{rcl} f (x) & = & f (- 1) \\ = & - 8 \end{array}$

The required value of $a$ is:

$\begin{array}{rcl} f (x) & = & a {(x - h)}^{2} + k \\ f (- 1) & = & a {(- 1 - 1)}^{2} + 4 鈰� 鈰� 鈰� (x = - 1, h = 1, k = 4, f (- 1) = - 8) \\ - 8 & = & a {(- 2)}^{2} + 4 \\ - 8 & = & 4 a + 4 \\ 4 a & = & - 12 \\ a & = & \frac{- 12}{4} \\ a & = & - 3 \end{array}$

Step 3. Determine the value of b and c.

$\begin{array}{rcl} f (x) & = & a {(x - h)}^{2} + k \\ f (x) & = & - 3 {(x - 1)}^{2} + 4 鈰� 鈰� (h = 1, k = 4, a = - 3) \\ f (x) & = & - 3 (x^{2} - 2 x + 1) + 4 \\ f (x) & = & - 3 x^{2} + 6 x - 3 + 4 \\ f (x) & = & - 3 x^{2} + 6 x + 1 \end{array}$

Compare the function $f (x) = - 3 x^{2} + 6 x + 1$ with $f (x) = a x^{2} + b x + c$ .

Hence, $a = - 3, b = 6$ and $c = 1$ .

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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 $(1, 4)$ and passes through the point $(- 1, - 8)$ . Findrole="math" localid="1646894617982" $a, b$ and $c$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the value of a.

Step 3. Determine the value of b and c.

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91影视

The graph of the function fx=ax2+bx+chas vertex at 1,4and passes through the point -1,-8. Findrole="math" localid="1646894617982" a,bandc.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the value of a.

Step 3. Determine the value of b and c.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Decision Maths

Applied Mathematics

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

The graph of the function $f (x) = a x^{2} + b x + c$ has vertex at $(1, 4)$ and passes through the point $(- 1, - 8)$ . Findrole="math" localid="1646894617982" $a, b$ and $c$ .