what is x square - 3 x + Y=0
Get the complete, step-by-step math solution for: "what is x square - 3 x + Y = 0". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Identify the equation type
The given equation is x2−3x+y=0. This equation involves two variables, x and y, and the highest power of x is 2, while the highest power of y is 1. This structure indicates that it represents a parabola.
Step 2: Rearrange the equation to standard form
To better understand the parabola's properties, we can rearrange the equation to express y in terms of x. By moving the x terms to the right side of the equation, we get y=−x2+3x. This is the standard form for a parabola opening downwards.
Step 3: Find the roots (x-intercepts)
To find where the parabola intersects the x -axis, we set y=0. This gives us −x2+3x=0. Factoring out −x, we get −x(x−3)=0. This implies that x=0 or x=3. So, the parabola crosses the x -axis at (0,0) and (3,0).
Step 4: Find the vertex
For a parabola in the form y=ax2+bx+c, the x -coordinate of the vertex is given by x=−2ab. Here, a=−1 and b=3, so x=−2(−1)3=23. Substituting this value back into the equation, we find the y -coordinate: y=−(23)2+3(23)=−49+29=49. Thus, the vertex is at (23,49).