The problem asks us to identify the vertex and axis of symmetry of a given parabola from its graph, and to determine whether the parabola opens upwards or downwards.

GeometryParabolaVertexAxis of SymmetryGraphing
2025/7/3

1. Problem Description

The problem asks us to identify the vertex and axis of symmetry of a given parabola from its graph, and to determine whether the parabola opens upwards or downwards.

2. Solution Steps

Step 1: Identify the vertex. The vertex is the lowest point of the parabola. From the graph, we can see that the vertex is at the point (3,3)(-3, -3).
Step 2: Identify the axis of symmetry. The axis of symmetry is a vertical line that passes through the vertex of the parabola. The equation of a vertical line is of the form x=cx = c, where cc is a constant. Since the vertex is at (3,3)(-3, -3), the axis of symmetry is the vertical line x=3x = -3.
Step 3: Determine the direction the parabola opens. From the graph, we can see that the parabola opens upwards.

3. Final Answer

The vertex of the parabola is (3,3)(-3, -3).
The axis of symmetry is x=3x = -3.
The parabola opens upwards.

Related problems in "Geometry"

The problem asks to express the vectors $\overline{MK}$, $\overline{NL}$, $\overline{NK}$, and $\ove...

VectorsVector AdditionGeometric Vectors
2025/7/3

We are given two diagrams containing vectors. We need to find which options are equal to the resulta...

VectorsVector AdditionVector Decomposition
2025/7/3

The problem asks us to find the slope of the line shown in the graph.

Linear EquationsSlopeCoordinate Geometry
2025/7/3

The problem asks whether the endpoints of the given graph are included or not. A closed circle indic...

Graph AnalysisInterval NotationEndpoints
2025/7/3

The problem asks to find the slope of a line given two points on the line: $(-10, -9)$ and $(-6, -5)...

SlopeCoordinate GeometryLinear Equations
2025/7/3

We are given the area of a square as 81 square meters, and we are asked to find the side length of t...

AreaSquareSide LengthGeometry
2025/7/2

We are asked to find the area of a square, given that its side length is $0.7$ meters. We are asked ...

AreaSquareUnit Conversion
2025/7/2

We are given a shaded shape on a grid. Each square on the grid has a side length of 1 cm. We are ask...

AreaApproximationGridShapes
2025/7/2

The problem states that $Z$ is the centroid of triangle $TRS$. Given that $TO = 7b + 5$, $OR = 13b -...

CentroidTriangleMidpointAlgebraic EquationsLine Segments
2025/7/1

We are given that $m\angle ACT = 15a - 8$ and $m\angle ACB = 74$. Also, S is the incenter of $\trian...

Angle BisectorIncenterTriangleAnglesAlgebraic Manipulation
2025/7/1