The real solutions to a quadratic equation correspond to which points on the graph?

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Multiple Choice

The real solutions to a quadratic equation correspond to which points on the graph?

Explanation:
Real solutions to a quadratic are the x-values that make the expression zero. On the graph of y = ax^2 + bx + c, these occur where the curve crosses the x-axis, at the x-intercepts (points with y = 0). So the real solutions correspond to the x-intercepts. If the parabola touches the axis, there is one real root; if it crosses twice, there are two; if it never touches, there are no real solutions. For example, y = x^2 - 5 has intercepts at (√5, 0) and (-√5, 0). The y-intercept is where x = 0, the axis of symmetry is the vertical line x = -b/(2a), and the vertex is the highest or lowest point of the parabola.

Real solutions to a quadratic are the x-values that make the expression zero. On the graph of y = ax^2 + bx + c, these occur where the curve crosses the x-axis, at the x-intercepts (points with y = 0). So the real solutions correspond to the x-intercepts. If the parabola touches the axis, there is one real root; if it crosses twice, there are two; if it never touches, there are no real solutions. For example, y = x^2 - 5 has intercepts at (√5, 0) and (-√5, 0). The y-intercept is where x = 0, the axis of symmetry is the vertical line x = -b/(2a), and the vertex is the highest or lowest point of the parabola.

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