Question

Find the y-intercept, the equation of the axis of symmetry, and the x-coordinate

of the vertex.
f(x) = 2x² - 4x + 3

Answer 1

The y-intercept is 3, the equation of the axis of symmetry is x = 1, and the x-coordinate of the vertex is 1.

Step-by-step explanation:

The y-intercept, or the point where the graph intersects the y-axis, can be found by setting x = 0 in the equation. So, for the equation f(x) = 2x² - 4x + 3, when x = 0, we have f(0) = 3. Therefore, the y-intercept is 3.

The equation of the axis of symmetry can be found by using the formula x = -b/2a. In this case, a = 2 and b = -4. So, the axis of symmetry equation is x = -(-4)/(2*2) = 1. The axis of symmetry is x = 1.

The x-coordinate of the vertex can be found using the equation x = -b/2a. In this case, a = 2 and b = -4. So, the x-coordinate of the vertex is x = -(-4)/(2*2) = 1.