Pretty stuck on this paper,someone help out? an explanation would be appreciated as well!

Answers

Answer 1

Answer:

I can help you with graphing quadratics in intercept form. Here's a step-by-step guide:

Step 1: Identify the intercepts

The intercepts are the points where the parabola crosses the x-axis and y-axis. In intercept form, the x-intercepts are given by the factors of the quadratic expression. For example, in the equation f(x) = 2(x+4)(x+6), the x-intercepts are -4 and -6. To find the y-intercept, set x = 0 and solve for y.

Step 2: Find the vertex

The vertex is the point where the parabola reaches its maximum or minimum value. The x-coordinate of the vertex is the average of the x-intercepts. In the equation f(x) = 2(x+4)(x+6), the x-intercepts are -4 and -6, so the x-coordinate of the vertex is (-4 + -6)/2 = -5. To find the y-coordinate of the vertex, substitute the x-coordinate into the equation and solve for y.

Step 3: Plot the intercepts and vertex

Mark the intercepts and vertex on the coordinate plane.

Step 4: Sketch the parabola

Draw a smooth curve that passes through the intercepts and vertex. The parabola should be symmetric about the vertical line passing through the vertex.

Example:

Let's graph the equation f(x) = 2(x+4)(x+6).

Step 1: Identify the intercepts

The x-intercepts are -4 and -6. To find the y-intercept, set x = 0 and solve for y:

f(0) = 2(0+4)(0+6) = 48

So the y-intercept is (0, 48).

Step 2: Find the vertex

The x-coordinate of the vertex is (-4 + -6)/2 = -5. To find the y-coordinate of the vertex, substitute x = -5 into the equation:

f(-5) = 2(-5+4)(-5+6) = 2

So the vertex is (-5, 2).

Step 3: Plot the intercepts and vertex

Plot the intercepts (-4, 0), (-6, 0), and (0, 48), and the vertex (-5, 2) on the coordinate plane.

Step 4: Sketch the parabola

Draw a smooth curve that passes through the intercepts and vertex. The parabola should be symmetric about the vertical line passing through the vertex.

The graph of the equation f(x) = 2(x+4)(x+6) is a parabola that opens upwards and has intercepts at (-4, 0), (-6, 0), and (0, 48). The vertex of the parabola is at (-5, 2).

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A parabola is defined by the equation (x − 5)2 = 12(y + 2). In which direction will the parabola open?

Answers

Since the equation is in the form:
(1/a)(y – k) = (x – h)2

Then, the parabola will open either upward or downward. To tell which direction will the parabola open, the coefficient of the term:
(y – k)
must be inspected.

The coefficient is 12 and it is a positive number, therefore, the parabola will open upward.

How do you prove (3x+2)2 is equivalent to (3x+6)(3x-2)+16i have tried expanding the brackets but I'm still really stuck
thankyou in advance

Answers

$(3x+2)^2=9x^2+12x+4\n\n (3x+6)(3x-2)+16=\n9x^2-6x+18x-12+16=\n9x^2+12x+4$

Which of the following is a result of shifting a circle with equation (x + 3)2 + (y - 2)2 = 36 right 3 units?A. The y-coordinate of the center of the circle decreases by 3.
B. The y-coordinate of the center of the circle increases by 3.
C. The x-coordinate of the center of the circle increases by 3.
D. Both the x- and y-coordinates of the center of the circle increase by 3.