Consider the quadratic equation y=x 2 +12x+35. Find the x−intercepts of the graph of the quadratic relationship.
Question
Consider the quadratic equation .
Find the x−intercepts of the graph of the quadratic relationship.
Solution
To find the x-intercepts of the graph of the quadratic equation y = x^2 + 12x + 35, we need to set y to 0 and solve for x.
Step 1: Set y to 0 0 = x^2 + 12x + 35
Step 2: Solve for x This is a quadratic equation in the form of ax^2 + bx + c = 0. We can solve for x using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / 2a.
In this equation, a = 1, b = 12, and c = 35.
Step 3: Substitute a, b, and c into the quadratic formula x = [-12 ± sqrt((12)^2 - 4135)] / 2*1 x = [-12 ± sqrt(144 - 140)] / 2 x = [-12 ± sqrt(4)] / 2 x = [-12 ± 2] / 2
Step 4: Solve for x x = [-12 + 2] / 2 = -10 / 2 = -5 x = [-12 - 2] / 2 = -14 / 2 = -7
So, the x-intercepts of the graph of the quadratic equation y = x^2 + 12x + 35 are x = -5 and x = -7.
Similar Questions
Consider the quadratic equation y=x 2 −2x+3. Find the x−intercepts of the graph of the quadratic relationship.
What are the x-intercepts and the vertex of the parabola represented by y = 2x2 - 5x -12?
Find the vertex of quadratic relation by completing the square.y = x2 + 12x + 30
Which of the following represents the x-intercepts and the vertex of the quadratic relation y = −x2 − 6x + 27?
Find the equation of the following parabola which has vertex at (4,−1) and 𝑥-intercepts at 𝑥=12√+4 and 𝑥=4−12√.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.