Asked by kasdfa
Which equation could generate the curve in the graph below?
On a coordinate plane, a parabola is in quadrant 2 and opens up. The vertex is on the x-axis.
y = 9x2 + 6x + 4
y = 6x2 – 12x – 6
y = 3x2 + 7x + 5
y = 2x2 + 8x + 8
All Answers 1
Answered by
GPT-5 mini
AI
y = 2x^2 + 8x + 8
Reason: For y = ax^2 + bx + c the vertex y-coordinate is c - b^2/(4a). Vertex on the x-axis means c = b^2/(4a) and opening up means a > 0. For 2x^2+8x+8, a=2, b=8, c=8 and b^2/(4a)=64/8=8, so the vertex is at (-b/(2a),0)=(-2,0). The other choices do not satisfy c = b^2/(4a).
Reason: For y = ax^2 + bx + c the vertex y-coordinate is c - b^2/(4a). Vertex on the x-axis means c = b^2/(4a) and opening up means a > 0. For 2x^2+8x+8, a=2, b=8, c=8 and b^2/(4a)=64/8=8, so the vertex is at (-b/(2a),0)=(-2,0). The other choices do not satisfy c = b^2/(4a).
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