Is there a way to solve this system of equations without using the quadratic formula (or graphing)?

f(x) = –2/3 x + 4

g(x) = 3(x + 2)^2 – 4

How many solutions does the system above have?

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Posts Tagged: parabolas

# Is there a way to solve this system of equations without using the quadratic formula (or graphing)?

# What is the x-coordinate of the vertex of the graph of y = -6x^2 + 3x + 8

# PWN the SAT Parabolas drill explanation p. 325 #10

# A tennis ball is thrown upward from the ground and its height, h, is given by the equation h=22t – t^2. Some kids are sitting on the roof of a building that stands 21 feet tall. If the kids are sitting in such a position that they cannot see the ball until it reaches the height of the roof, for how many seconds of the tennis ball’s flight can the kids see the ball? A- 18 B-20 C-21 D-22

# A question from the May 2018 SAT (Section 4 #18)

# Can you please explain Question 11, Test 6, section 3?

# PWN p. 157 #8

# Test 6 Section 3 #13

# Test 2 Section 4 #7

# PSAT #1, Section 3, #13

# Question number 6 from the Parabola chapter

# Parabola D in the xy-plane has equation x – 2y^2 – 8y – 11 = 0…

# Practice Test 4, Section 3, Number 11 (No Calc)

# How do you do Test 5 Section 4 #35?

# Test 6 calculator section #34 please!

Is there a way to solve this system of equations without using the quadratic formula (or graphing)?

f(x) = –2/3 x + 4

g(x) = 3(x + 2)^2 – 4

How many solutions does the system above have?

Huge shortcut here if you just know that for a parabola in standard ax^2 + bx + c form, the x-coordinate of the vertex will be at –b/(2a). In this case, that means it’s at –3/(2(–6)) = 3/12 = ¼. from Tumblr https://ift.tt/2CRW93a

PWN the SAT Parabolas drill explanation p. 325 #10: The final way to solve: If we are seeking x=y, since the point is (a,a), why can you set f(x) = 0? You start out with the original equation in vertex form, making y=a and x=a, but halfway through you change to y=0 (while x is still = a). How can we be solving the equation when we no longer have a for both x and y?

Basically, the question is: how many seconds is h greater than 21? (This tennis ball is being thrown on a planet other than Earth, by the way. I challenge anyone to throw a tennis ball that stays in the air anywhere near as long as this one does.) To figure it out, solve for the (more…)

A question from the May 2018 SAT (Section 4 #18)

kx + y = 1

y = -x² + k

In the system of equations above, k is a constant. When the equations are graphed in the xy-plane, the graphs intersect at exactly two points. Which of the following CANNOT be the value of k?

A. 3

B. 2

C. 1

D. 0

Hi Mike, Can you please explain Question 11, Test 6, section 3 ? I know the parabola opens downward, but I’m confused after that. Thanks.

In PWN p. 159 (p. 157 later printing) #8

In the xy-plane, where a and b are constants, the graphs …

The question does not specify that a and b are positive values. If one or both were negative, wouldn’t that change the answer?

Test 6 Section 3 #13

Test 2 Section 4 #7

PSAT #1, Section 3, #13

Hi, Mike! Can you explain the second way we can approach question number 6 from the Parabola chapter? (The two points where the higher y-coordinate is also farther from the line of symmetry.) It would be great if you can provide an example. Thank you.

Parabola D in the xy-plane has equation x – 2y^2 – 8y – 11 = 0. Which equation shows the x-intercept(s) of the parabola as constants or coefficients?

A) x = 2y^2 + 8y + 11

B) x = 2(y + 2)^2 + 3

C) x – 3 = 2(y + 2)^2

D) y = – √(x – 3)/2 – 2

The answer is A) which makes me think this is really just a “do you know the definition of this term” kind of question (similar to official practice test 4.4.28). Can you explain for those weak in this? TIA!

Practice Test 4, Section 3, Number 11 (No Calc)

How do you do Test 5 Section 4 #35?

Test 6 calculator section #34 please!