Final answer:
The correct x-intercepts of the quadratic equation y = 4x² - 7x - 8 are closest to x = -1 and x = 2, corresponding to option a), assuming the given answer choices are rounded or there is an error in the original question.
Step-by-step explanation:
The question deals with finding the x-intercepts of the given parabola y = 4x² - 7x - 8. The x-intercepts are the values of x where the parabola crosses the x-axis, which means setting y to zero and solving the quadratic equation. To find the x-intercepts, we use the quadratic formula x = [-b ± √(b² - 4ac)] / (2a), where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
For the given quadratic equation, a = 4, b = -7, and c = -8, we substitute these into the quadratic formula:
• x = [(7) ± √((-7)² - 4 × 4 × (-8))] / (2 × 4)
• x = [7 ± √(49 + 128)] / 8
• x = [7 ± √(177)] / 8
• x = [7 ± 13.304] / 8
• Two solutions for x: (7 + 13.304) / 8 or (7 - 13.304) / 8
• x = 20.304 / 8 or x = -6.304 / 8
• x = 2.54 or x = -0.79
The solutions do not exactly match the options provided, indicating a potential miscalculation. The correct intercepts must be the ones closest to the solutions found, thus the closest answer to the calculated x-intercepts is option a) x = -1, x = 2, assuming the given options are rounded figures or there was an error in the original question.