Final answer:
The y-intercept of the equation y = (3/4)(x^2 - x - 3) is at (0, -2.25). The axis of symmetry is the line x = 0.5. These can be determined using standard formulas for quadratic equations.
Step-by-step explanation:
To find the y-intercept and axis of symmetry for the quadratic equation y = \( \frac{3}{4}(x^2 - x - 3) \), we need to identify the components of the equation that correspond to these features. A quadratic equation in the form y = ax^2 + bx + c has a y-intercept at (0, c), therefore, substituting x=0 in our equation, the y-intercept for this equation is y = \( \frac{3}{4}(0^2 - 0 - 3) \) = -\( \frac{9}{4} \) or (0, -2.25). The axis of symmetry can be found using the formula x = -\( \frac{b}{2a} \) where a and b are coefficients from the quadratic term and the linear term, respectively. In our case, a = \( \frac{3}{4} \) and b = -\( \frac{3}{4} \), thus the axis of symmetry is x = -\( \frac{-\( \frac{3}{4} \)}{2 \times \( \frac{3}{4} \)} \) = \( \frac{1}{2} \) or x = 0.5. This is a vertical line passing through the vertex of the parabola.