Question

Y equals X squared -2x add 5

Answer 1

Explanation:

y = x^2 -2x + 5

Since this quadratic is positive, this will face upwards, where there is a minimum and no maximum.

You can first find the y-intercept, by inputting 0 for x.

y = x^2 -2x + 5

y = 0^2 - 2(0) + 5

y = 5

Then, you can input a random number for x that is greater than or less than 0 to see which side of the y-axis the function is at.

Inputting 1 gives 4, which is less than (0, 5), meaning the graph is on the right side of the y-axis.

Finding more points will yield more information.

You can convert this quadratic equation into a binomial to visualize the graph, using the quadratic formula.

The attached shows the input for the quadratic formula. This will give you your a and b values in the binomial format.

y = (x + a)(x + c)

Answer 2

Answer: 1

Explanation:

The equation Y = X^2 - 2X + 5 is a quadratic function in standard form. The graph of a quadratic function is a parabola. The vertex of the parabola is at the point (h, k), where h and k are the x and y coordinates of the vertex, respectively.

To find the vertex of the parabola, we can use the formula h = -b/2a and k = f(h), where a, b, and c are the coefficients of the quadratic function. In this case, a = 1, b = -2, and c = 5. Therefore, h = 1 and k = 4.

The vertex of the parabola is at the point (1, 4). The parabola opens upwards because the coefficient of X^2 is positive. The axis of symmetry is the vertical line that passes through the vertex. The equation of the axis of symmetry is X = h, which in this case is X = 1.