Domain and range of a quadratic in vertex form
State the range of a quadratic function given in vertex form y = a(x-h)^2+k. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
State the range of the function.
y = −(x + 4)2 + 5
- y ≥ 5
- y ≤ −5
- y ≤ 5
- x ≤ 5
Answer: y <= 5
See one solved, step by step
State the range of the function.
y = −(x - 2)2 + 5
- y ≤ 5
- x ≤ 5
- y ≥ 5
- y ≤ −5
📘 Worked solution
1Vertex form: y = a(x - h)2 + k, so the vertex is (2, 5).h and k are read directly from the equation — here h = 2 and k = 5.
2a = −1, which is negative, so the parabola opens downward.The sign of a controls which way the graph opens.
3Domain: x is any real number. Range: y ≤ 5.A downward parabola never goes above its vertex, so y is always at most 5.
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