How do you graph #y = x² + 2x – 4#?

Answer 1

Graph y = x^2 + 2x - 4

To graph a parabola, find a few critical points: Axis of symmetry --> #x = -b/2a = - 1# Vertex --> #x = -b/2a = -1# y = f(-1) = 1 - 2 - 4 = -5 y-intercept --> make x = 0 --> y = -4 x-intercept --> solve y = 0 --> #x^2 + 2x - 4 = 0.# #D = d^2 = b^2 - 4ac = 4 + 16 = 20 #--># d = +- 2sqrt5# #x = -2/2 +- 2sqrt5/2= -1 +- sqrt5# graph{x^2 + 2x - 4 [-10, 10, -5, 5]}
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Answer 2

To graph the equation y = x² + 2x - 4, you can follow these steps:

  1. Identify the vertex of the parabola using the formula for the vertex of a quadratic function: Vertex = (-b/2a, f(-b/2a)), where a, b, and c are the coefficients of the quadratic equation ax² + bx + c.

  2. Determine whether the parabola opens upwards or downwards based on the sign of the coefficient of x² (a). If a > 0, the parabola opens upwards; if a < 0, the parabola opens downwards.

  3. Find the y-intercept by substituting x = 0 into the equation and solving for y.

  4. Determine the x-intercepts (if any) by setting y = 0 and solving the resulting quadratic equation.

  5. Plot the vertex, y-intercept, and x-intercepts on the coordinate plane.

  6. Determine additional points on the graph by choosing values of x and calculating the corresponding values of y using the equation.

  7. Connect the points to form a smooth curve, representing the graph of the quadratic function.

If you follow these steps, you will accurately graph the equation y = x² + 2x - 4.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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