Y=x2 +0,3
It looks like you have provided the equation of a quadratic function in the form \( y = x^2 + 0.3 \). Here’s a breakdown of the function:
Shape of the Graph: This equation represents a parabola that opens upwards since the coefficient of \( x^2 \) is positive.
Vertex: The vertex of the parabola occurs at the point where \( x = 0 \) (because there are no linear \( x \) terms in this equation). Plugging \( x = 0 \) into the equation gives: \[ y = 0^2 + 0.3 = 0.3 \] So, the vertex is at the point \( (0, 0.3) \).
Y-intercept: The y-intercept is the point where the graph intersects the y-axis, which occurs at \( x = 0 \): \[ y = 0^2 + 0.3 = 0.3 \] Thus, the y-intercept is \( (0, 0.3) \), which is the same as the vertex in this case.
X-intercepts: To find the x-intercepts, set \( y = 0 \) and solve for \( x \): \[ 0 = x^2 + 0.3 \implies x^2 = -0.3 \] Since this leads to a negative number under the square root, there are no real x-intercepts. Therefore, the graph does not cross the x-axis.
Graph: The graph is a U-shaped curve that is centered vertically at \( y = 0.3 \) and does not intersect the x-axis. It will extend infinitely both upwards and to the sides.
If you have specific questions or need further analysis, feel free to ask!
