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Look at the system of inequalities. $\newline$ $y \leq -x + 4$ $\newline$ $x \geq 0$ $\newline$ $y \geq 0$ $\newline$ The solution set is the triangular region where all the inequalities are true. $\newline$ What are the vertices of that triangular region? $\newline$ (,) $\newline$ (,) $\newline$ (,)

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Find the focus or directrix of a parabola

Full solution

Q. Look at the system of inequalities.

\newline

y \leq -x + 4

\newline

x \geq 0

\newline

y \geq 0

\newline

The solution set is the triangular region where all the inequalities are true.

\newline

What are the vertices of that triangular region?

\newline

(____,____)

\newline

(____,____)

\newline

(____,____)

Find Intersection with X-Axis: First, let's find the intersection of $y = -x + 4$ and the x-axis ( $y = 0$ ). $\newline$ Set $y = 0$ in $y = -x + 4$ and solve for $x$ . $\newline$ $0 = -x + 4$ $\newline$ $x = 4$ $\newline$ So, one vertex is at $(4, 0)$ .
Find Intersection with Y-Axis: Next, find the intersection of $y = -x + 4$ and the y-axis ( $x = 0$ ). $\newline$ Set $x = 0$ in $y = -x + 4$ and solve for $y$ . $\newline$ $y = -0 + 4$ $\newline$ $y = 4$ $\newline$ So, another vertex is at $(0, 4)$ .
Find Third Vertex: The third vertex is the intersection of the x-axis and y-axis, which is the origin. $\newline$ So, the third vertex is at $(0, 0)$ .

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What is the focus of the parabola

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\newline

\text{[A]up}

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\text{[B]down}

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What is the vertex of the parabola

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\newline

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Question

The equation of a circle is

x^{2}+(y+4)^{2}=1

. What are the center and radius of the circle?

\newline

1

\newline

(A) The center is

(-4,0)

and the radius is

1

\newline

(B) The center is

(4,0)

and the radius is

1

\newline

(C) The center is

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(D) The center is

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Question

y=(x-3)(x+9)

\newline

The given equation is graphed in the

x y

-plane. Which of the following are

x

-intercepts of the graph?

\newline

1

\newline

-3

-9

\newline

-3

9

\newline

3

-9

\newline

3

9

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Question

y=2 x^{2}-5 x+7

is graphed in the

x y

-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?

\newline

1

\newline

x

\newline

y

\newline

x

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\newline

y

-coordinate of the vertex

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Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant