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3 years ago

Use the graph of f(x) = x2 to write an equation for the function represented by each graph.

Mathematics

1 answer:

MariettaO [177]3 years ago

7 0

Answer:

y = -(x + 2)² + 1

Step-by-step explanation:

Parent function given in the graph is a quadratic function,

f(x) = x²

Since, graph is opening downwards transformed function of the preimage will be,

g(x) = -x²

This transformed function is shifted further by 2 units left horizontally and 1 unit upwards.

Therefore, rule for the transformation will be,

g(x) → h[(x + 2), (y + 1)]

By this rule transformed function will be,

h(x) = -(x + 2)²+ 1

Equation of the curve will be,

y = -(x + 2)² + 1

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What is the solution to the system of equations? y = A system of equations. Y equals StartFraction 2 over 3 EndFraction x plus 3

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Answer:

The solution to the given system of equations is (-2, $\frac{5}{3}$ )

Therefore the values of x and y are x=-2 and $y=\frac{5}{3}$

Step-by-step explanation:

Given equations can be written as

$y=\frac{2}{3}x+3\hfill (1)$

$x=-2x+3x=-2\hfill (2)$

Solving equation(2) we get

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Substitute x=-2 in equation (1) we get

$y=\frac{2}{3}(-2)+3$

$=-\frac{4}{3}+3$

$=\frac{-4+9}{3}$

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Anuta_ua [19.1K]

Answer:

1.) Y = 5/3 X + 4

2.) Y = 9/4 X - 27/4

Step-by-step explanation:

Given the slope and the coordinate, linear equation of a line can be expressed by using general linear equation. Which is

Y = MX + C

Where the

Slope M = 5/3

Coordinate = (-3,-1) in which

X = -3, Y = -1

Substitute X, Y and M into the general linear equation to achieve C

-1 = 5/3(-3) + C

-1 = - 5 + C

C = 5 - 1

C = 4

Substitute C and M back into the general linear equation.

Therefore, the equation of the line given the slope and a point through the line passes 5/3, and (-3,-1) to be

Y = 5/3 X + 4

2.) Also,

Slope M = 9/4

Coordinate = (3,0) where X = 3, Y = 0

Substitute X, Y and M into the general linear equation to obtain C

0 = 9/4 (3) + C

C = - 27/4

Substitutes C and M back into the general linear equation

Therefore, the equation of the line given the slope and a point through the line passes 9/4 and (3,0)

Y = 9/4 X - 27/4

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