Question

Please Help !!! its a math problem What is the range of the quadratic equation whose graph contains the following points?

Vertex at (0, 4)
Other points on graph are (-2, 0), (-1, 3), (1, 3) and (2, 0).

Answer 1

Range of a Quadratic Function

The range tells us the possible y-values that occur in the function.

When describing the range, we can write an inequality using y.

• Examples: y > 6, y ≤ 10

When describing the range of a quadratic function, we typically use the ≥ or ≤ symbols when writing the inequality.

To write the range of a quadratic function,

1. Find the vertex
2. Determine whether the parabola opens up or down
3. Set y ≥ or ≤ the y-coordinate of the vertex

Solving the Question

We're given:

• Vertex at (0,4)
• Other points on the graph: (-2,0), (-1,3), (1,3), (2,0)

Because we're directly given the vertex, we just have to determine now whether the parabola opens up or down.

• If the other points on the graph always have a lower y-coordinate value, then the graph opens down
• If the other points on the graph always have a greater y-coordinate value, then the graph opens up

The other points that fall on the graph that we're given all have a lower y-coordinate value than 4, that means this parabola opens down.

Therefore, all other y-values for the function will be less than 4.

Therefore, y ≤ 4.

Answer

y ≤ 4